Abstract
Combination of weighted weibull distribution proposed by Ramadan and beta distribution gives a better distribution (beta-weighted weibull distribution) than each of them individually in terms of the estimate of their characteristics in their parameters. The combination was done by using the logic of beta function by Jones. We investigated in the new proposed beta-weighted weibull distribution some basic properties including moments, moment generating functions, survival rate function, and hazard rate function, skewness, and kurtosis, coefficient of variation, asymptotic behaviors and estimation of parameters. The proposed model is much more flexibility and has better representation of data than weighted weibull distribution. A real data set is used to illustrate the importance the potentiality of the new model.
Highlights
Combination of weighted weibull distribution proposed by Ramadan and beta distribution gives a better distribution than each of them individually in terms of the estimate of their characteristics in their parameters
The article is outlined as follows: In section 2, we introduce the new proposed beta weighted weibull distribution (BWW) including the density and distribution function, the asymptotic behaviors, survival rate, hazard rate function, etc. and special models
The study of skew models is useful in modeling skew data that brings about the new proposed distribution which generalizes the weighted weibull distribution and the new distribution includes as special submodels other distribution
Summary
Combination of weighted weibull distribution proposed by Ramadan and beta distribution gives a better distribution (beta-weighted weibull distribution) than each of them individually in terms of the estimate of their characteristics in their parameters. We investigated in the new proposed beta-weighted weibull distribution some basic properties including moments, moment generating functions, survival rate function, and hazard rate function, skewness, and kurtosis, coefficient of variation, asymptotic behaviors and estimation of parameters. The proposed model is much more flexibility and has better representation of data than weighted weibull distribution. The weighted with parameters and defined in (1) using the logit of beta function by weibull distribution is used to adjust the probabilities of the events Jones [4]. The article is outlined as follows: In section 2, we introduce the new proposed beta weighted weibull distribution (BWW) including the density and distribution function, the asymptotic behaviors, survival rate, hazard rate function, etc. Moment and moment generating function is discussed in section 3.Section 4 carries the parameter estimation, in section 5, empirical application to real data set and section 6 gives concluding remarks
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