`scipy.stats._continuous_distns:truncpareto_gen`

source: /scipy/stats/_continuous_distns.py :10459

Signature

   class     truncpareto_gen (    momtype    =  1   ,    a    =  None   ,    b    =  None   ,    xtol    =  1e-14   ,    badvalue    =  None   ,    name    =  None   ,    longname    =  None   ,    shapes    =  None   ,    seed    =  None     )

Members

Summary

An upper truncated Pareto continuous random variable.

Extended Summary

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Notes

The probability density function for truncpareto is:

f (x, b, c) = \frac{b}{1 - c ^{- b}} \frac{1}{x ^{b + 1}}

for $b \neq = 0$ , $c > 1$ and $1 \leq x \leq c$ .

truncpareto takes b and c as shape parameters for $b$ and $c$ .

Notice that the upper truncation value $c$ is defined in standardized form so that random values of an unscaled, unshifted variable are within the range [1, c]. If u_r is the upper bound to a scaled and/or shifted variable, then c = (u_r - loc) / scale. In other words, the support of the distribution becomes (scale + loc) <= x <= (c*scale + loc) when scale and/or loc are provided.

The fit method assumes that $b$ is positive; it does not produce good results when the data is more consistent with negative $b$ .

truncpareto can also be used to model a general power law distribution with PDF:

f (x; a, l, h) = \frac{a}{h ^{a} - l ^{a}} x^{a - 1}

for $a \neq = 0$ and $0 < l < x < h$ . Suppose $a$ , $l$ , and $h$ are represented in code as a, l, and h, respectively. In this case, use truncpareto with parameters b = -a, c = h / l, scale = l, and loc = 0.

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Aliases

scipy.stats._continuous_distns.truncpareto_gen