Applied Mathematics & Information Sciences

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Weighted distributions have great practical importance in mathematics, probability and statistics. In this study a new discrete distribution which is a weighted version of Discretized Fréchet-Weibull distribution (DFWD), known as Weighted Discretized Fréchet-Weibull distribution (WDFWD), is proposed. It has been shown that the distribution is unimodal, positively skewed and suitable for modelling with overdispersed count data sets. This distribution has bathtub shape and decreasing hazard rate function. Various statistical properties and simulation of the proposed distribution are obtained. The estimation of parameters have been handled by the method of maximum likelihood estimation. Finally, the proposed model has been fitted to three real life data sets to test its goodness of fit. And to show its efficacy it is being compared with Discretized Fréchet-Weibull distribution, discrete generalized Weibull, discrete generalized inverse Weibull, discrete Burr and discrete Rayleigh distribution. It is established that the weighted version of DFWD gives better fit than the parent model DFWD, which indicates the importance of weighted distribution.

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