The log-logistic distribution is widely used in survival analysis when the failure rate function presents a unimodal shape. Based on the log-logistic and Kumaraswamy distributions , we introduce Keywords: Kumaraswamy distribution, Reliability Function, Maximum Likelihood Estimation, Order Statistics 1. Introduction Kumaraswamy (1980) proposed a two-parameter Kumaraswamy distribution on (0, 1), and denoted by Kum (θ,α). Its cumulative distribution function is given by the Kumaraswamy distribution. MLE is a popular method but not always the best one. In practice, most of the sample sizes of real data are not big enough, so that MLE-based large sample asymptotic intervals may be invalid for small sample (DiCiccio and Efron, 1996). Kumaraswamy distribution is characterized by the following probability density function, f(x;a,b) = a b x^{a-1} (1-x^a)^{b-1}where the domain is x \in (0,1) with two shape parameters a,b > 0. Kumaraswamy: (Weighted) MLE of Kumaraswamy Distribution in kyoustat/T4mle: What the Package Does Using Title Case Inference on the log-eponentiated Kumaraswamy distribution 167 (EK) distribution. we derived the LEK distribution. This distribution extended the generalized exponential and double generalized exponential distribution. We proposed maximum likelihood estimation of the model of parameters. Nadarajah A new four parameter lifetime distribution called Weibull-Kumaraswamy distribution is proposed by applying the generator Weibull- Generalized family of distribution. The Kumaraswamy distribution is similar to the Beta distribution but has the key advantage of a closed-form cumulative distribution function. In this paper we present the estimation of Kumaraswamy distribution parameters based on Generalized Order Statistics (GOS) using Maximum Likelihood Estimators (MLE). We proved that the In this paper, the estimation of the unknown parameters of the kumaraswamy distribution is considered using both simple random sampling (SRS) and ranked set sampling (RSS) techniques. The estimation is based on maximum likelihood estimation and Bayesian estimation methods. A simulation study is made to compare the resultant estimators in A KUMARASWAMY DISTRIBUTION BASED ON HYBRID PROGRESSIVE CENSORED SAMPLE Authors: Akram Kohansal { Department of Statistics, Imam Khomeini International University, maximum likelihood estimation (MLE), approximation maximum likelihood estima-tion (AMLE) and two Bayesian approximation estimates due to the lack of explicit of the MLE estimators under the corresponding generated models while some data applications are also illustrated. Keywords— Kumaraswamy distribution, quantile function, Simulation, maximum likelihood estimation. Mathematics Subject Classification. 60E05, 62E15, 62F10. 1 Introduction
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