Estimation and prediction for the Kumaraswamy-inverse Rayleigh distribution based on records

Abstract

In this paper, estimators for the parameters of the Kumaraswamy-inverse Rayleigh distribution based on record values are obtained. These estimators are derived using the maximum likelihood and Bayesian methods. The Bayesian estimators are derived under the well-known squared error (SE) loss function. Prediction of the future sth record value is derived using the maximum likelihood and Bayesian methods. Simulation study is conduct to illustrate the findings.

The Kumaraswamy Exponentiated U-Quadratic Distribution: Properties and Application

“…The method of generalization of distributions by the Kumaraswamy-G generator proposed by [1] is one of the preferable techniques in distribution theory and was considered by many authors in recent years. For instance, the Kumaraswamy-Weibull distribution [2], Kumaraswamy binomial [3], Kumaraswamy generalized gamma [4], Kumaraswamy-Gumbel [5], Kumaraswamy generalized half-normal [6], Kumaraswamy log-logistic [7], Kumaraswamy-Birnbaum-Saunders [8], Kumaraswamy inverse Weibull [9], Kumaraswamy double inverse exponential [10], Kumaraswamy power series [11], Kumaraswamy-Pareto [12], Kumaraswamy generalized linear failure rate [13], Kumaraswamy exponentiated Pareto [14], Kumaraswamy quasi-Lindley [15], Kumaraswamy generalized Pareto [16], Kumaraswamy-Burr XII distribution [17], Kumaraswamy generalized exponentiated Pareto [18], Kumaraswamy generalized Lomax [19], Kumaraswamy geometric [20], Kumaraswamy half-Cauchy distrbution [21], Kumaraswamy generalized Rayleigh [22], Kumaraswamy-Dagum distribution [23], Kumaraswamy inverse Rayleigh [24], Kumaraswamy inverse exponential [25], Kumaraswamy -Kumaraswamy [26], Kumaraswamy transmuted exponentiated modified Weibull [27], Kumaraswamy odd loglogistic [28], Kumaraswamy skew-normal [29].…”

The type II Topp Leone generalized inverse Rayleigh distribution

“…Lot of works have been studied in the literature on IR distribution. Gharraph (1993) and Hassan et al (2010) (2) Recently, Elgarhy et al (2018) studied Type II top leone generated (TIITL-G) family of distributions. The cdf of TIITL -G is given by:…”

Classical and Bayesian estimation for Topp Leone inverse Rayleigh distribution

“…Many works have been discussed in the literature on IR distribution. Gharraph [2] and Hassan et al [4] estimated the parameters using classical and Bayesian estimation…”