The power function distribution is a flexible model often used for the analysis of income distribution data, lifetime data, and modeling of failure processes. For example, one use of the distribution is in reliability assessment of electrical components and semiconductor devices . One strength of the power function distribution is its mathematical simplicity, compared to more complex distributions like the Weibull distribution.
Theoretically, the power function distribution is a special case of the beta distribution , and the Pearson type I distribution. It also has an inverse relationship with the standard Pareto distribution ; moments of the power function distribution are the negative moments of the Pareto distribution .
Power-Function Distribution PDF
Note on “Power Functions”
A power function has the form f(x) = axp. There are an infinite number of possible power functions, depending on your choice of scaling factor a and exponent p. Each power function has an associated distribution (or graph). Therefore, the term power function distribution could refer to one of these distributions (rather than “the” power function distribution described above).
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Stephanie Glen. "Power Function Distribution" From StatisticsHowTo.com: Elementary Statistics for the rest of us! https://www.statisticshowto.com/power-function-distribution/
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