Kumaraswamy distribution

About: Kumaraswamy distribution is a research topic. Over the lifetime, 213 publications have been published within this topic receiving 3393 citations. The topic is also known as: Kumaraswamy's double bounded distribution.

On Size Biased Kumaraswamy Distribution

Abstract: In this paper, we introduce and study the size-biased form of Kumaraswamy distribution. The Kumaraswamy distribution which has drawn considerable attention in hydrology and related areas was proposed by Kumarswamy. The new distribution is derived under sizebiased probability of sampling taking the weights as the variate values. Various distributional and characterizing properties of the model are studied. The methods of maximum likelihood and matching quantiles estimation are employed to estimate the parameters of the proposed model. Finally, we apply the proposed model to simulated and real data sets.

Statistical Inference for Kumaraswamy Distribution Based on Generalized Order Statistics with Applications

Abstract: In this paper, non-Bayesian and Bayesian approaches are used to obtain point and interval estimation of the shape parameters, the reliability and the hazard rate functions of the Kumaraswamy distribution. The estimators are obtained based on generalized order statistics. The symmetric and asymmetric loss functions are considered for Bayesian estimation. Also, maximum likelihood and Bayesian prediction for a new observation are found. The results have been specialized to Type II censored data and the upper record values. Comparisons are made between Bayesian and non-Bayesian estimates via Monte Carlo simulation. Moreover, the results are applied on real hydrological data.

The McDonald arcsine distribution: a new model to proportional data

Abstract: We propose a new three-parameter continuous model called the McDonald arcsine distribution, which is a very competitive model to the beta, beta type I and Kumaraswamy distributions for modelling rates and proportions. We provide a mathematical treatment of the new distribution including explicit expressions for the density function, moments, generating and quantile functions, mean deviations, two probability measures based on the Bonferroni and Lorenz curves, Shannon entropy, Renyi entropy and cumulative residual entropy. Maximum likelihood is used to estimate the model parameters and the expected information matrix is determined. An application of the proposed model to real data shows that it can give consistently a better fit than other important statistical models.

Statistical Properties of Kumaraswamy Exponentiated Gamma Distribution

Abstract: The Exponentiated Gamma (EG) distribution is one of the important families of distributions in lifetime tests. In this paper, a new generalized version of this distribution which is called kumaraswamy Exponentiated Gamma (KEG) distribution is introduced. A new distribution is more flexible and has some interesting properties. A comprehensive mathematical treatment of the KEG distribution is provided. We derive the r th moment and moment generating function of this distribution. Moreover, we discuss the maximum likelihood estimation of the distribution parameters. Finally, an application to real data sets is illustrated.

Inference on the Kumaraswamy distribution

Abstract: Many lifetime distribution models have successfully served as population models for risk analysis and reliability mechanisms. The Kumaraswamy distribution is one of these distributions which is particularly useful to many natural phenomena whose outcomes have lower and upper bounds or bounded outcomes in the biomedical and epidemiological research. This article studies point estimation and interval estimation for the Kumaraswamy distribution. The inverse estimators (IEs) for the parameters of the Kumaraswamy distribution are derived. Numerical comparisons with maximum likelihood estimation and biased-corrected methods clearly indicate the proposed IEs are promising. Confidence intervals for the parameters and reliability characteristics of interest are constructed using pivotal or generalized pivotal quantities. Then, the results are extended to the stress–strength model involving two Kumaraswamy populations with different parameter values. Construction of confidence intervals for the stress–stren...