On discrete Weibull Distribution

الملخص EN

Most of the Weibull models studied in the literature were appropriate for modelling a continuous random variable which assume the variable takes on real values over the interval [0, ∞].

One of the new studies in statistics is when the variables takes on discrete values.

The idea was first introduced by Nakagawa and Osaki, as they introduced discrete Weibull distribution with two shape parameters q and p where 0 < q < 1 and P > 0.

Weibull models for modelling discrete random variables assume only non-negative integer values.

Such models are useful for modelling for example ; the number of cycles to failure when components are subjected to cyclical loading.

Discrete Weibull models can be obtained as the discrete counter parts of either the distribution function or the failure rate function of the standard Weibull model.

Which lead to different models.

This paper discusses the discrete model which is the counter part of the standard two-parameter Weibull distribution.

It covers the determination of the probability mass function, cumulative distribution function, survivor function, hazard function, and the pseudo-hazard function.