# Questions tagged [pareto-distribution]

The Pareto distribution is a power distribution which was initially invented to describe the distribution of income but has found application in many other areas.

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### Applying Tangent Lines to Log-Scaled Data for Outlier Detection: Seeking Statistical Theories and Models

I've analyzed the view counts for a YouTube channel's videos (just for example), sorting them by views (on the left) and drawing a tangent line to approximate the central trend on a logarithmic scale (...
76 views

### Bayes estimator of possion distribution with Pareto prior

Consider a random sample of size $n$ following the possion distribution with parameter $\ln \theta$, that is $$f(x|\theta)=\frac{(\ln\theta)^x}{\theta x!}, x=0,1,2,\cdots$$ and the prior of the ...
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### R: Getting Wrong Profile Likelihood Confidence Interval Estimates

I am trying to estimate the profile likelihood confidence interval (CI) of the parameters ($\xi$, $\sigma$) of the Generalized Pareto Distribution (GPD). However, the lower estimate (left CI) of $\xi$ ...
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### Number of ten millionaires in a country [closed]

Given that I know the number of billionaires B and millionaires M in a society and that wealth is distributed in as a Pareto, how do I figure out the number of people with more than 10 million dollars?...
144 views

### Extending the 80/20 rule

I have seen comments on the web that because the 80/20 rule is fractal, it applies to the sub groups. In other words, if the top 20% of causes drive 80% of outcomes, then the top 4% of causes must ...
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1 vote
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### Chebyshev's inequality for Pareto distribution (3 sigma rule)

According to the Chebyshev's inequality, if we take any distribution, we get >88.8889% of data in +-3 sigma interval. For a normal distribution it is 99.97%. How to calculate the interval for a ...
535 views

### Neyman-Pearson Lemma for Pareto Distribution [duplicate]

I have the following problem. Let $X_1, ..., X_n$ represent a random sample taken from a population with CDF given by $$F(x;\beta) = 1 - \frac{\beta}{x}, ~~ x \geq \beta > 0.$$ Based on the this ...
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### Method of moments and MLE estimates for Lomax (Pareto Type 2)

I have this dataset, on which I am supposed to fit Lomax distribution with MM and MLE. Lomax pdf is: $$f(x|\alpha, \lambda) = \frac{\alpha\lambda^\alpha}{\left(\lambda+x\right)^{\alpha+1}}$$ For MM, ...
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645 views

### Understanding Hypothesis tests for a Pareto distribution

I'm writing an essay that's looking at the presence of the Pareto Principle in data. Unfortunately, as a consequence of interest, I've picked a topic that involves statistical analysis well above what ...
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1 vote