Discrete Weibull distribution

This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: "Discrete Weibull distribution" – news · newspapers · books · scholar · JSTOR (August 2024) (Learn how and when to remove this message)

Discrete Weibull
Parameters	${\displaystyle \alpha >0}$ scale ${\displaystyle \beta >0}$ shape
Support	${\displaystyle x\in \{0,1,2,\ldots \}}$
PMF	${\displaystyle \exp \left[-\left({\frac {x}{\alpha }}\right)^{\beta }\right]-\exp \left[-\left({\frac {x+1}{\alpha }}\right)^{\beta }\right]}$
CDF	${\displaystyle 1-\exp \left[-\left({\frac {x+1}{\alpha }}\right)^{\beta }\right]}$

In probability theory and statistics, the discrete Weibull distribution is the discrete variant of the Weibull distribution. The Discrete Weibull Distribution, first introduced by Toshio Nakagawa and Shunji Osaki, is a discrete analog of the continuous Weibull distribution, predominantly used in reliability engineering. It is particularly applicable for modeling failure data measured in discrete units like cycles or shocks. This distribution provides a versatile tool for analyzing scenarios where the timing of events is counted in distinct intervals, making it distinctively useful in fields that deal with discrete data patterns and reliability analysis. The discrete Weibull distribution is infinitely divisible only for ${\displaystyle 0<\beta \leq 1}$.^[1]