Abstract
We introduce and characterize a new family of distributions, Marshall-Olkin discrete uniform distribution. The natures of hazard rate, entropy, and distribution of minimum of sequence of i.i.d. random variables are derived. First order autoregressive (AR (1)) model with this distribution for marginals is considered. The maximum likelihood estimates for the parameters are found out. Also, the goodness of the distribution is tested with real data.
Highlights
Marshall and Olkin [1] introduced a new method for adding a parameter to a family of distributions with application to the exponential and Weibull families
The following theorem gives a characterization of minimum of a sequence of i.i.d. random variables following MODU distribution
Since mode > median > mean, the data exhibits negative skewness with m.l.e. of θ > 1 and it is observed that the distribution is unimodal; MODU distribution is supposed to give a better fit than uniform distribution
Summary
Marshall and Olkin [1] introduced a new method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Jose and Alice [2] discussed Marshall-Olkin family of distributions and their applications in time series modeling and reliability. Jose and Krishna [3] have developed Marshall-Olkin extended uniform distribution. If F(x) is the survival function of a distribution, by Marshall-Olkin method, we get another survival function G(x), by adding a new parameter θ to it. An AR (1) model with new Marshall-Olkin discrete uniform distribution is discussed . The maximum likelihood estimate (m.l.e.) for the parameters is found out and, in the last section, the goodness of the distribution is tested with a real life data
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