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Crypto blogs are sites or extensions of websites that treat topics relating to crypto developments and events. These platforms offer detailed information on crypto updates, review crypto products, and analyze crypto topics. These platforms could fixate on a particular crypto niche or explore a variety of topics relating to cryptocurrency as a whole. The former, which are specialized blogs, create contents that center around a particular crypto sector. Therefore, they are ideal for people invested in the crypto niche in question.

On the other hand, there are crypto blogs that have no restrictions as regards the range of topics they cover. As such, they are appealing to a larger demographic. However, it is unlikely that this variation of crypto blogs would provide a deep analysis of topics as niche-selective publications would.

Besides, we have begun to witness an explosion of corporate blogs, which crypto firms manage and solely function as brand optimizers. Likewise, there are personal blogs, owned by crypto enthusiasts willing to share their insight on trending crypto themes.

In this article, you'll learn Top 20 crypto blogs.

**1. Ethereum Blog**

Name | Description | Pros | Cons | Website |

Ethereum Blog | The official Ethereum blog is just as what you would expect to find! It’s designed with upmost simplicity in mind and contains extremely well curated content from professionals with deep tech experience. Expect to primarily read about news and announcements related to Ethereum with in depth technical explanations in every piece of content. There is no need to explain how to use this blog site as its one simple streamlined feed of their latest content right on the home screen. There is nothing to push other than links at the top to their official Ethereum website, Bug Bounty Program and Ethereum Research Forum. And that’s it. If you want to find content related to Ethereum and read the latest news, come here. If you don’t have an interest in that, you probably shouldn’t visit this site as there is literally nothing else on it. | This blog is incredibly simple and straight forward. Content on Ethereum is very educational for beginners and tech experts | If you don’t like Ethereum you won’t like this blog, pretty simple. | Website |

**2. Trezor Blog**

Name | Description | Pros | Cons | Website |

Trezor Blog | Trezor is a very popular hardware wallet service and product that gives its users a massive security advantage over those who use online wallet services. Trezor is one of the top competitors in this niche and are certainly one of the most widely recognized hardware wallets available. Their blog is situated on Medium and consists mostly of content related to the advancements of their technology and services. You’ll find some pretty in-depth information related to their hardware and software developments that a lot of individuals who have tech backgrounds may find interesting. Aside from tech articles, there are a few general crypto blog posts relating to coins being integrated into Trezor and some general tutorials on wallets, accounts, addresses, blockchain, etc. | Trezor blog pieces are well curated and designed The blogs are easy to read and offer information relating to people of all experience levels | Content isn’t published everyday or even every other day. | Website |

**3. Binance Blog**

Name | Description | Pros | Cons | Website |

Binance Blog | Binance's has a highly active blog that they produce content so that readers can keep up to date with developments for the company and other topics related to the company. Binance operates a number of organizations outside of the exchange such as an over-the-counter market, separate fiat to cryptocurrency exchanges, a wallet, and a not-for-profit foundation. The blog is used as a platform to keep those interested up to date with developments across all of these platforms. Points to note related to the main exchange are also published on the blog such as when new cryptocurrencies or tokens are being listed on to the exchange. The blog is available in seven languages including Spanish, Italian, and Chinese. The blog is very recent and has only been operating since December 2018 but it is highly active so far. It is not uncommon for several pieces to be posted within one day. The content published is also released on the Twitter pages related to the different binance entities. | A convenient way for users to keep up to date with developments happening across the different organizations binance operates The blog is highly active The blog is available in a number of different languages | The blog has only started releasing content very recently Users may prefer to keep up to date with developments via social media | Website |

**4. Coinbase blog**

Name | Description | Pros | Cons | Website |

Coinbase blog | Coinbase is arguably one of the most popular cryptocurrency exchanges and online wallet services there is. They’ve been around for awhile and have established a lot of trust. Users primarily use coinbase to purchase their first crypto because coinbase makes it incredibly simply and easy to do so.
| The blog is well organized and extremely easy to use. If you’re looking for quality information leading into the crypto world, the blog section at Coinbase is a great place to start. Top quality writers contribute to the blog making it a great reading experience. | Since coinbase is a business and likely hires most of these bloggers, I am sure the content is biased so just keep this in mind when receiving important information through this blog. | Website |

**5. Kraken Blog**

Name | Description | Pros | Cons | Website |

Kraken Blog | Kraken is another major cryptocurrency exchange and online digital wallet service that primarily serves the US market. Kraken was created by the original cofounders of Facebook, the Winklevoss twins. Kraken isn’t usually referred to as a big player in the world of crypto exchanges but I wouldn’t underestimate their ability to take a huge position in the future. The blog on Kraken is primarily focused on themselves but they do offer a little content outside of their own activities. Using the link above, you’ll immediate see a list of blogs with no particular order. Their respective categories are listed above each piece but ordering them doesn’t seem to be possible. Upon taking a quick browse, I really only see announcement style blogs that are focused on what Kraken is doing and will be doing in the near future. I also see product blogs that are completely focused on a service or product Kraken is developing and introducing. There does seem to be a couple blogs categorized as “uncategorized” that can offer various content, but these are few and far between. Overall, the blog interface is clean and well designed with plenty of updated content to read through. If you’re not interested directly in what Kraken is doing, then you probably won’t find this blog of much value. The blog is almost entirely focused only on their business entity alone. | There is content updated here often The blog is a great place to follow Kraken and understand what they’re doing next. | The blog focuses solely on Kraken and offers little outside content. | Website |

**6. Bitfinex Blog**

Name | Description | Pros | Cons | Website |

Bitfinex Blog | A major behemoth exchange must have a blog and of course, Bitfinex is no exception. Bitfinex has been the center of a lot of controversy and drama, making this one exchange that is quite interesting to read about. From the drama with Tether (USDT) to the moving of their main office to multiple scandals and hacks, Bitfinex seems to always have an interesting tail to tell. The blog display and design is just as good as the exchanges display. It’s got a very well designed look and feel, something Bitfinex’s users love about the exchanges interface. Beyond its physical characteristics, the blog seems to focus on announcements, changelogs, API, Events, and tutorials. They also have a cute little profiles section where they write a short piece about the major team members and employees from time to time, but these are few and far between. Most of whats found in Bitfinex’s blog is content solely focused on Bitfinex themselves. From announcement blogs detailing their next big move to changelogs outlining technical updates, the blogs will keep you up to date with this massive player in the world of crypto exchanges. Aside from Bitfinex related content, there isn’t any. Just about everything found in the blog is 100% relatable to Bitfinex in someway or another so if you’re not interested in what Bitfinex is up to, you won’t find interest in their blog either. | This is a major exchange and if you’re wanting to be a crypto expert, it may be a good idea to keep an eye on this blog for important updates USDT is directly related to Bitfinex and plays a major role in the crypto market. This blog talks about it often and will continue talking about it in the future, so keep an eye on that. | There is no content outside of Bitfinex related discussion at all. | Website |

**7. BitPay Blog**

Name | Description | Pros | Cons | Website |

BitPay Blog | Bitpay is a very well-designed blog that is clean and easy to use. Immediately upon entering the sight you will be prompted with a huge blue button asking you to subscribe for blog updates! If receiving emails about new blogs is your thing, that may be a good option for you! This blog looks to be an all-around great place to read up on this merchant-crypto software. If you accept crypto on a website or have future ambitions to do so, you should most certainly be paying attention to this blog. Bitpay is one of the top crypto merchant software’s available and with that, comes great insight from their top tier position in the niche. | Great content from a leading crypto merchant software company | If you aren’t interested in accepting crypto as payments this probably isn’t the place for you as there is really nothing other than Bitpay related content. | Website |

**8. Cex Blog**

Name | Description | Pros | Cons | Website |

Cex Blog | Cex.io is a pretty popular exchange for cryptocurrency assets and also offers an online wallet service. The Cex blog is designed in a very simplistic modern configuration with a block style feed. Users will immediately notice the lack of extra stuff lying around the page. On the blog interface, there are literally only blogs, which provides a very seamless experience and clean display. The styling of Cex overall is just beautiful and really portrays the future of modern website design. | Beautiful display Easy to use and browse around for content | Content is good but it’s not regularly updated. | Website |

**9. Gemini Blog**

Name | Description | Pros | Cons | Website |

Gemini Blog | Gemini is another major digital asset exchange primarily focused on the US markets. You can buy and sell almost any major cryptocurrency here and the exchange also offers a digital wallet service for you to store, send, and receive digital assets. Gemini was founded by the ever so popular Facebook “founders”, the Winklevoss twins. Gemini’s blog is incredibly well curated and is updated often. | This blog makes keeping up with the exchange easy You’ll learn the ends and outs of the Gemini exchange with well curated and professionally written content | There is little to no information that doesn’t relate to Gemini directly. | Website |

**10. Changelly Blog**

Name | Description | Pros | Cons | Website |

Changelly Blog | Changelly is another cryptocurrency and online wallet services exchange that offers hundreds of cryptos for purchase, selling, storage, and sending. The blog is situated directly on their site via WordPress and offers what seems to be just a handful of posts on news only related to them and their services, with the exception of a few of tutorials. The design is quite modern and clean and the blog overall is very easy to navigate. On the right side you’ll find a “tags” section where you can filter and choose the content you wish to see. There are 50+ tags to choose from and the default setting selects them all. | Changelly hosts a well-designed blog with a very simplistic user experience I would recommend visiting this blog if you’re new to crypto and you’ve chosen Changelly as your primary exchange. There are a few blog posts that are tutorial like in nature and may offer some helpful information | There doesn’t seem to be a whole ton of content being posted here. Expect only 2-3 posts a month. | Website |

**11. Coinjar Blog**

Name | Description | Pros | Cons | Website |

Coinjar Blog | Coinjar is claimed to be “Australia’s most popular Bitcoin wallet” and hosts a very intuitive crypto wallet for several different digital assets. They have a blog where you can read all about it. Arriving on the site will punch you right in the face with a massive photo which is part of their most recent news articles. Under that you’ll find a list the most recent content produced on the blog. The site is very well designed and quite clean. The articles are easy to scroll through and the content seems to range drastically. Content is updated at least once a week, sometimes more, and seems to be written by professionals in their fields. The content ranges in experience levels but I think everyone from beginner to expert crypto levels can find useful and comprehendible content here. | The blog is tidy and easy to use with lots of great content Content is updated at least once per week | If you don’t use Coinjar this probably isn’t the blog for you | Website |

**12. Coinatmradar Blog**

Name | Description | Pros | Cons | Website |

Coinatmradar Blog | Coin ATM Radar is a software service and app that paints a beautiful picture of all the locations you can find a cryptocurrency ATM. The Coin ATM Radar blog paints a beautiful picture of all of their news, announcements, updates, and information regarding Crypto ATMs. That last one you don’t see very often which makes this blog pretty interesting! | This blog was a really nice change of pace from all of the general crypto blogs that all post the same things. Easy to use and well-designed interface with biweekly content releases. | You’ll be sad if the map shows no ATMs in your country or area. I was :( If you aren’t into crypto ATMs you wont be into this blog. | Website |

**13. Coingate Blog**

Name | Description | Pros | Cons | Website |

Coingate Blog | Coingate is “Your Gateway to Bitcoin Payments”. Yes, since that isn’t very explanatory I will elaborate what they do! Coingate is essentially a software design company that focuses on providing eCommerce plugins for accepting crypto in online storefronts. In their blog you will find a very simple, and I mean simple as it gets display of news and content. Of course, most of the content is solely based on Coingate and what they’ve been up to. With that said, if you don’t like Coingate and/or you don’t have a need for eCommerce crypto plugins, you can probably stop reading now and forget about this blog forever. | The site is very clean and well designed. There is biweekly content that is informative and high quality. | If you have no interest in eCommerce then you may not find much value in reading this blog. | Website |

**14. Shapeshift blog**

Name | Description | Pros | Cons | Website |

Shapeshift blog | Shapeshift is a cryptocurrency swapping platform that enables its users to easily and quickly swap between assets. Their swapping technology can be found hidden inside a lot of apps and wallets, so you may have used them without even knowing! Given a fantastic software base service, they must have a fantastic blog spot as well, right? Right! This blog is great and encompasses tons of different topics inside a plethora of categories. The blog overall is a pretty familiar design as it’s similar to most crypto blogs and doesn’t have any mind-blowing functionalities that will throw you for a loop. It is well designed and the interface is very clean. You will see an updated news feed on the default setting which is All Categories. | Easy to use and well designed Has tons of information regarding Shapeshift and the general crypto environment | Some people dislike Shapeshift and I’d imagine they would dislike this blog too. | Website |

**15. Bitedge Blog**

Name | Description | Pros | Cons | Website |

Bitedge Blog | Bitedge is a great place to throw away your crypto in the hopes of your favorite sports teams taking the W. If giving away crypto is your prerogative, please message me instead of gambling it away! Jokes aside, this website doesn’t actually have gambling. It just tries to help you with a few tools such as odds comparisons and bitcoin gambling blogs, which is what we’re here to discuss. | Looks like a good sight with tools and information to help you place bets on sports! | The content is not written by professionals but more so by hobbyists. | Website |

**16. Cryptomining Blog**

Name | Description | Pros | Cons | Website |

Cryptomining Blog | This blog has very easy to understand content for both beginners and advanced miners. | The site is incredibly easy to use. There is TONS of helpful information here for users of all experience levels. | The website just feels a little dirty to me compared to other crypto blogs. | Website |

**17. Wirexapp Blog**

Name | Description | Pros | Website |

Wirexapp Blog | Wirex is an application-based software that allows you easily to buy, store, and sell crypto with no fees. There is content ranging from just about every crypto category you can think of. From trading to wallet tutorials, this blog covers it all. At the bottom of the page you’ll find a massive list of tags which you can click on to find very specific articles. | The best cryptocurrency articles? Maybe not, but they are really good The website is really easy to use and has a unique interface | Website |

**18. Purse Blog**

Name | Description | Pros | Cons | Website |

Purse Blog | Purse is the infamous crypto to Amazon bridge created and designed to enable Amazon shoppers to earn crypto. How do they do this? Crypto holders will create a list of items they want from Amazon and name their “price” in crypto. Amazon shoppers then purchase this item and trade it for the crypto offered by the buyer. | The content that is available is certainly well written and helpful. | The content isn’t up to date and there are categories lacking actual blog posts. Is it even a category if there are no posts inside of it? | Website |

**19. Paxful Blog**

Name | Description | Pros | Cons | Website |

Paxful Blog | Paxful is basically a payment system that claims to be Paypal + uber. Their blog is incredibly colorful compared to most other crypto blog sites but is equally as well designed and simple to use. Of course it’s just a simple WordPress site like most of the others as well, so the layout is very similar and should be familiar to any blog lovers. | The blog couldn’t be any easier to use as there are no buttons, links, etc to worry about. The content is updated roughly twice a month. | If you aren’t a Paxful fan you probably won’t like the blog. | Website |

Read more: **Top 50 Cryptocurrency News Sites You Need Know**

*Top exchanges for token-coin trading. Follow instructions and make unlimited money*

☞ Binance ☞ FTX ☞ Poloniex ☞ Bitfinex ☞ Huobi ☞ MXC ☞ ByBit ☞ Gate.io

Thank for visiting and reading this article! Please share if you liked it!

#cryptocurrency #blockchain #bitcoin #news #blogs

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March 25, 2021 Deepak@321 0 Comments

Welcome to my blog, In this article, we will learn the top 20 most useful python modules or packages and these modules every Python developer should know.

Hello everybody and welcome back so in this article I’m going to be sharing with you 20 Python modules you need to know. Now I’ve split these python modules into four different categories to make little bit easier for us and the categories are:

**Web Development****Data Science****Machine Learning****AI and graphical user interfaces.**

Near the end of the article, I also share my personal favorite Python module so make sure you stay tuned to see what that is also make sure to share with me in the comments down below your favorite Python module.

#python #packages or libraries #python 20 modules #python 20 most usefull modules #python intersting modules #top 20 python libraries #top 20 python modules #top 20 python packages

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Germany was the first country to recognize #Bitcoins as “units of value” and that they could be classified as a “financial instrument.”

Legal regulation for the decentralized industry in Germany is ongoing. Now, 16% of the German population 18 to 60 are #crypto investors.

These people who own #cryptocurrencies or have traded cryptocurrencies in the past six months.

41% of these #crypto investors intend to increase the share of their investments in #crypto in the next six months. Another 13% of Germans are #crypto-curious.

They intend to invest in #cryptocurrencies too. Yet, only 23% of the #crypto-curious said they are highly likely to invest, with the rest remaining hesitant.

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This package contains a variety of functions from the field robust statistical methods. Many are estimators of location or dispersion; others estimate the standard error or the confidence intervals for the location or dispresion estimators, generally computed by the bootstrap method.

Many functions in this package are based on the R package WRS (an R-Forge repository) by Rand Wilcox. Others were contributed by users as needed. References to the statistics literature can be found below.

This package requires `Compat`

, `Rmath`

, `Dataframes`

, and `Distributions`

. They can be installed automatically, or by invoking `Pkg.add("packagename")`

.

`tmean(x, tr=0.2)`

- Trimmed mean: mean of data with the lowest and highest fraction`tr`

of values omitted.`winmean(x, tr=0.2)`

- Winsorized mean: mean of data with the lowest and highest fraction`tr`

of values squashed to the 20%ile or 80%ile value, respectively.`tauloc(x)`

- Tau measure of location by Yohai and Zamar.`onestep(x)`

- One-step M-estimator of location using Huber's ψ`mom(x)`

- Modified one-step M-estimator of location (MOM)`bisquareWM(x)`

- Mean with weights given by the bisquare rho function.`huberWM(x)`

- Mean with weights given by Huber's rho function.`trimean(x)`

- Tukey's trimean, the average of the median and the midhinge.

`winvar(x, tr=0.2)`

- Winsorized variance.`wincov(x, y, tr=0.2)`

- Winsorized covariance.`pbvar(x)`

- Percentage bend midvariance.`bivar(x)`

- Biweight midvariance.`tauvar(x)`

- Tau measure of scale by Yohai and Zamar.`iqrn(x)`

- Normalized inter-quartile range (normalized to equal σ for Gaussians).`shorthrange(x)`

- Length of the shortest closed interval containing at least half the data.`scaleQ(x)`

- Normalized Rousseeuw & Croux Q statistic, from the 25%ile of all 2-point distances.`scaleS(x)`

- Normalized Rousseeuw & Croux S statistic, from the median of the median of all 2-point distances.`shorthrange!(x)`

,`scaleQ!(x)`

, and`scaleS!(x)`

are non-copying (that is,`x`

-modifying) forms of the above.

`trimse(x)`

- Standard error of the trimmed mean.`trimci(x)`

- Confidence interval for the trimmed mean.`msmedse(x)`

- Standard error of the median.`binomci(s,n)`

- Binomial confidence interval (Pratt's method).`acbinomci(s,n)`

- Binomial confidence interval (Agresti-Coull method).`sint(x)`

- Confidence interval for the median (with optional p-value).`momci(x)`

- Confidence interval of the modified one-step M-estimator of location (MOM).`trimpb(x)`

- Confidence interval for trimmed mean.`pcorb(x)`

- Confidence intervale for Pearson's correlation coefficient.`yuend`

- Compare the trimmed means of two dependent random variables.`bootstrapci(x, est=f)`

- Compute a confidence interval for estimator`f(x)`

by bootstrap methods.`bootstrapse(x, est=f)`

- Compute a standard error of estimator`f(x)`

by bootstrap methods.

`winval(x, tr=0.2)`

- Return a Winsorized copy of the data.`idealf(x)`

- Ideal fourths, interpolated 1st and 3rd quartiles.`outbox(x)`

- Outlier detection.`hpsi(x)`

- Huber's ψ function.`contam_randn`

- Contaminated normal distribution (generates random deviates).`_weightedhighmedian(x)`

- Weighted median (breaks ties by rounding up). Used in scaleQ.

For location, consider the `bisquareWM`

with k=3.9σ, if you can make any reasonable guess as to the "Gaussian-like width" σ (see dispersion estimators for this). If not, `trimean`

is a good second choice, though less efficient. Also, though the author personally has no experience with them, `tauloc`

, `onestep`

, and `mom`

might be useful.

For dispersion, the `scaleS`

is a good general choice, though `scaleQ`

is very efficient for nearly Gaussian data. The MAD is the most robust though less efficient. If scaleS doesn't work, then shorthrange is a good second choice.

The first reference on scaleQ and scaleS (below) is a lengthy discussion of the tradeoffs among scaleQ, scaleS, shortest half, and median absolute deviation (MAD, see BaseStats.mad for Julia implementation). All four have the virtue of having the maximum possible breakdown point, 50%. This means that replacing up to 50% of the data with unbounded bad values leaves the statistic still bounded. The efficiency of Q is better than S and S is better than MAD (for Gaussian distributions), and the influence of a single bad point and the bias due to a fraction of bad points is only slightly larger on Q or S than on MAD. Unlike MAD, the other three do not implicitly assume a symmetric distribution.

To choose between Q and S, the authors note that Q has higher statistical efficiency, but S is typically twice as fast to compute and has lower gross-error sensitivity. An interesting advantage of Q over the others is that its influence function is continuous. For a rough idea about the efficiency, the large-N limit of the standardized variance of each quantity is 2.722 for MAD, 1.714 for S, and 1.216 for Q, relative to 1.000 for the standard deviation (given Gaussian data). The paper gives the ratios for Cauchy and exponential distributions, too; the efficiency advantages of Q are less for Cauchy than for the other distributions.

```
#Set up a sample dataset:
x=[1.672064, 0.7876588, 0.317322, 0.9721646, 0.4004206, 1.665123, 3.059971, 0.09459603, 1.27424, 3.522148,
0.8211308, 1.328767, 2.825956, 0.1102891, 0.06314285, 2.59152, 8.624108, 0.6516885, 5.770285, 0.5154299]
julia> mean(x) #the mean of this dataset
1.853401259
```

`tmean`

: trimmed mean```
julia> tmean(x) #20% trimming by default
1.2921802666666669
julia> tmean(x, tr=0) #no trimming; the same as the output of mean()
1.853401259
julia> tmean(x, tr=0.3) #30% trimming
1.1466045875000002
julia> tmean(x, tr=0.5) #50% trimming, which gives you the median of the dataset.
1.1232023
```

`winval`

: winsorize dataThat is, return a copy of the input array, with the extreme low or high values replaced by the lowest or highest non-extreme value, repectively. The fraction considered extreme can be between 0 and 0.5, with 0.2 as the default.

```
julia> winval(x) #20% winsorization; can be changed via the named argument `tr`.
20-element Any Array:
1.67206
0.787659
0.400421
0.972165
...
0.651689
2.82596
0.51543
```

`winmean`

, `winvar`

, `wincov`

: winsorized mean, variance, and covariance```
julia> winmean(x) #20% winsorization; can be changed via the named argument `tr`.
1.4205834800000001
julia> winvar(x)
0.998659015947531
julia> wincov(x, x)
0.998659015947531
julia> wincov(x, x.^2)
3.2819238397424004
```

`trimse`

: estimated standard error of the trimmed mean```
julia> trimse(x) #20% winsorization; can be changed via the named argument `tr`.
0.3724280347984342
```

`trimci`

: (1-α) confidence interval for the trimmed meanCan be used for paired groups if `x`

consists of the difference scores of two paired groups.

```
julia> trimci(x) #20% winsorization; can be changed via the named argument `tr`.
(1-α) confidence interval for the trimmed mean
Degrees of freedom: 11
Estimate: 1.292180
Statistic: 3.469611
Confidence interval: 0.472472 2.111889
p value: 0.005244
```

`idealf`

: the ideal fourths:Returns `(q1,q3)`

, the 1st and 3rd quartiles. These will be a weighted sum of the values that bracket the exact quartiles, analogous to how we handle the median of an even-length array.

```
julia> idealf(x)
(0.4483411416666667,2.7282743333333332)
```

`pbvar`

: percentage bend midvarianceA robust estimator of scale (dispersion). See NIST ITL webpage for more.

```
julia> pbvar(x)
2.0009575278957623
```

`bivar`

: biweight midvarianceA robust estimator of scale (dispersion). See NIST ITL webpage for more.

```
julia> bivar(x)
1.5885279811329132
```

`tauloc`

, `tauvar`

: tau measure of location and scaleRobust estimators of location and scale, with breakdown points of 50%.

See Yohai and Zamar *JASA*, vol 83 (1988), pp 406-413 and Maronna and Zamar *Technometrics*, vol 44 (2002), pp. 307-317.

```
julia> tauloc(x) #the named argument `cval` is 4.5 by default.
1.2696652567510853
julia> tauvar(x)
1.53008203090696
```

`outbox`

: outlier detectionUse a modified boxplot rule based on the ideal fourths; when the named argument `mbox`

is set to `true`

, a modification of the boxplot rule suggested by Carling (2000) is used.

```
julia> outbox(x)
Outlier detection method using
the ideal-fourths based boxplot rule
Outlier ID: 17
Outlier value: 8.62411
Number of outliers: 1
Non-outlier ID: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20
```

`msmedse`

: Standard error of the medianReturn the standard error of the median, computed through the method recommended by McKean and Schrader (1984).

```
julia> msmedse(x)
0.4708261134886094
```

`binomci()`

, `acbinomci()`

: Binomial confidence intervalCompute the (1-α) confidence interval for p, the binomial probability of success, given `s`

successes in `n`

trials. Instead of `s`

and `n`

, can use a vector `x`

whose values are all 0 and 1, recording failure/success one trial at a time. Returns an object.

`binomci`

uses Pratt's method; `acbinomci`

uses a generalization of the Agresti-Coull method that was studied by Brown, Cai, & DasGupta.

```
julia> binomci(2, 10) # # of success and # of total trials are provided. By default alpha=.05
p_hat: 0.2000
confidence interval: 0.0274 0.5562
Sample size 10
julia> trials=[1, 0, 1, 1, 0, 0, 1, 0, 0, 1, 1, 0]
julia> binomci(trials, alpha=0.01) #trial results are provided in array form consisting of 1's and 0's.
p_hat: 0.5000
confidence interval: 0.1768 0.8495
Sample size 12
julia> acbinomci(2, 10) # # of success and # of total trials are provided. By default alpha=.05
p_hat: 0.2000
confidence interval: 0.0459 0.5206
Sample size 10
```

`sint()`

Compute the confidence interval for the median. Optionally, uses the Hettmansperger-Sheather interpolation method to also estimate a p-value.

```
julia> sint(x)
Confidence interval for the median
Confidence interval: 0.547483 2.375232
julia> sint(x, 0.6)
Confidence interval for the median with p-val
Confidence interval: 0.547483 2.375232
p value: 0.071861
```

`hpsi`

Compute Huber's ψ. The default bending constant is 1.28.

```
julia> hpsi(x)
20-element Array{Float64,1}:
1.28
0.787659
0.317322
0.972165
0.400421
...
```

`onestep`

Compute one-step M-estimator of location using Huber's ψ. The default bending constant is 1.28.

```
julia> onestep(x)
1.3058109021286803
```

`bootstrapci`

, `bootstrapse`

Compute a bootstrap, (1-α) confidence interval (`bootstrapci`

) or a standard error (`bootstrapse`

) for the measure of location corresponding to the argument `est`

. By default, the median is used. Default α=0.05.

```
julia> ci = bootstrapci(x, est=onestep, nullvalue=0.6)
Estimate: 1.305811
Confidence interval: 0.687723 2.259071
p value: 0.026000
julia> se = bootstrapse(x, est=onestep)
0.41956761772722817
```

`mom`

and `mom!`

Returns a modified one-step M-estimator of location (MOM), which is the unweighted mean of all values not more than (bend times the `mad(x)`

) away from the data median.

```
julia> mom(x)
1.2596462322222222
```

`momci`

Compute the bootstrap (1-α) confidence interval for the MOM-estimator of location based on Huber's ψ. Default α=0.05.

```
julia> momci(x, seed=2, nboot=2000, nullvalue=0.6)
Estimate: 1.259646
Confidence interval: 0.504223 2.120979
p value: 0.131000
```

`contam_randn`

Create contaminated normal distributions. Most values will by from a N(0,1) zero-mean unit-variance normal distribution. A fraction `epsilon`

of all values will have `k`

times the standard devation of the others. Default: `epsilon=0.1`

and `k=10`

.

```
julia> srand(1);
julia> std(contam_randn(2000))
3.516722458797104
```

`trimpb`

Compute a (1-α) confidence interval for a trimmed mean by bootstrap methods.

```
julia> trimpb(x, nullvalue=0.75)
Estimate: 1.292180
Confidence interval: 0.690539 2.196381
p value: 0.086000
```

`pcorb`

Compute a .95 confidence interval for Pearson's correlation coefficient. This function uses an adjusted percentile bootstrap method that gives good results when the error term is heteroscedastic.

```
julia> pcorb(x, x.^5)
Estimate: 0.802639
Confidence interval: 0.683700 0.963478
```

`yuend`

Compare the trimmed means of two dependent random variables using the data in x and y. The default amount of trimming is 20%.

```
julia> srand(3)
julia> y2 = randn(20)+3;
julia> yuend(x, y2)
Comparing the trimmed means of two dependent variables.
Sample size: 20
Degrees of freedom: 11
Estimate: -1.547776
Standard error: 0.460304
Statistic: -3.362507
Confidence interval: -2.560898 -0.534653
p value: 0.006336
```

See `UNMAINTAINED.md`

for information about functions that the maintainers have not yet understood but also not yet deleted entirely.

Percentage bend and related estimators come from L.H. Shoemaker and T.P. Hettmansperger "Robust estimates and tests for the one- and two-sample scale models" in *Biometrika* Vol 69 (1982) pp. 47-53.

Tau measures of location and scale are from V.J. Yohai and R.H. Zamar "High Breakdown-Point Estimates of Regression by Means of the Minimization of an Efficient Scale" in *J. American Statistical Assoc.* vol 83 (1988) pp. 406-413.

The `outbox(..., mbox=true)`

modification was suggested in K. Carling, "Resistant outlier rules and the non-Gaussian case" in *Computational Statistics and Data Analysis* vol 33 (2000), pp. 249-258. doi:10.1016/S0167-9473(99)00057-2

The estimate of the standard error of the median, `msmedse(x)`

, is computed by the method of J.W. McKean and R.M. Schrader, "A comparison of methods for studentizing the sample median" in *Communications in Statistics: Simulation and Computation* vol 13 (1984) pp. 751-773. doi:10.1080/03610918408812413

For Pratt's method of computing binomial confidence intervals, see J.W. Pratt (1968) "A normal approximation for binomial, F, Beta, and other common, related tail probabilities, II" *J. American Statistical Assoc.*, vol 63, pp. 1457- 1483, doi:10.1080/01621459.1968.10480939. Also R.G. Newcombe "Confidence Intervals for a binomial proportion" *Stat. in Medicine* vol 13 (1994) pp 1283-1285, doi:10.1002/sim.4780131209.

For the Agresti-Coull method of computing binomial confidence intervals, see L.D. Brown, T.T. Cai, & A. DasGupta "Confidence Intervals for a Binomial Proportion and Asymptotic Expansions" in *Annals of Statistics*, vol 30 (2002), pp. 160-201.

Shortest Half-range comes from P.J. Rousseeuw and A.M. Leroy, "A Robust Scale Estimator Based on the Shortest Half" in *Statistica Neerlandica* Vol 42 (1988), pp. 103-116. doi:10.1111/j.1467-9574.1988.tb01224.x . See also R.D. Martin and R. H. Zamar, "Bias-Robust Estimation of Scale" in *Annals of Statistics* Vol 21 (1993) pp. 991-1017. doi:10.1214/aoe/1176349161

Scale-Q and Scale-S statistics are described in P.J. Rousseeuw and C. Croux "Alternatives to the Median Absolute Deviation" in *J. American Statistical Assoc.* Vo 88 (1993) pp 1273-1283. The time-efficient algorithms for computing them appear in C. Croux and P.J. Rousseeuw, "Time-Efficient Algorithms for Two Highly Robust Estimators of Scale" in *Computational Statistics, Vol I* (1992), Y. Dodge and J. Whittaker editors, Heidelberg, Physica-Verlag, pp 411-428. If link fails, see ftp://ftp.win.ua.ac.be/pub/preprints/92/Timeff92.pdf

Author: Mrxiaohe

Source Code: https://github.com/mrxiaohe/RobustStats.jl

License: MIT license

1624293660

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In this video, I’m showing you the 4 top ways to make passive income with cryptocurrencies in 2021. If you want to know how to make money with crypto, try out these 4 strategies that anyone can do! And make sure to watch until the end for a full explanation and walkthrough of how these methods work.

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12:22 - How much I have made and outro

📺 The video in this post was made by Charlie Chang

The origin of the article: https://www.youtube.com/watch?v=58WKjp57TXs

🔺 DISCLAIMER: The article is for information sharing. The content of this video is solely the opinions of the speaker who is not a licensed financial advisor or registered investment advisor. Not investment advice or legal advice.

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