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Moments are summaries of random variables' characteristics (e.g., location, scale). Use also for fractional moments.

1 vote
1 answer
38 views

Identifying candidate distributions with a desired set of qualitative characteristics

Is there a good way of finding candidate distributions based on a set of qualitative characteristics? For instance, at the moment I am looking for a continuous univariate two-parameter distribution, …
andrewH's user avatar
  • 3,247
2 votes
1 answer
1k views

Normalizing skewness with the Power or Box-Cox Transformation

Suppose I have a random sample drawn from an arbitrary strictly positive continuous distribution. Suppose moreover that I want to use the Box-Cox transform to zero out the skewness. Is there an explic …
andrewH's user avatar
  • 3,247
14 votes
1 answer
4k views

Constructing a continuous distribution to match $m$ moments

and skewness, excess kurtosis and higher moments = 0. … Instead of the usual central moments, I would accept a solution posed in terms of raw moments, or normalized moments, or cumulants if that makes the problem easier or produces a more interesting result …
andrewH's user avatar
  • 3,247
1 vote
0 answers
60 views

Partial quantile moments?

The integral from 0 to x* of x to the n times pdf(x) is usually called the nth partial moment function. Does the corresponding integral from 0 to y* of y to the n of the quantile density function, qdf …
andrewH's user avatar
  • 3,247
2 votes
0 answers
57 views

Is the maximum entropy distribution the same for conditional and unconditional moments?

From these observations, I have a set of moments, with the highest moment even. If the range were the real line (or the positive half-line? … My question is, if you have the same set of moments, only conditional on the observations being in the specified interval, is the maximum entropy distribution the same as if you had the unconditional moments
andrewH's user avatar
  • 3,247
5 votes
1 answer
42 views

How should I estimate the variance in a sample or population from the sample range?

Suppose I wish to know the variance within a sample or of the population from which it is drawn. However, I do not have true measurements for most of my "observations". Think of them as like wooden bl …
andrewH's user avatar
  • 3,247
0 votes
0 answers
14 views

By means of what distribution can I match the first n moments for arbitrary (i e. any) value...

Suppose I have the first n moments from some data set, either raw, centered or scaled, (or cumulants instead) whichever is more convenient for matching. … If not, what distribution allows me to match the largest number of the first n moments (or cumulants)? …
andrewH's user avatar
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3 votes
1 answer
81 views

Good parameter estimates vs good computed moment estimates

From the parameters I can numerically integrate and derive moments, if they exist. Are the good properties of the estimators inherited by such computed moments? …
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