Abstract
In this paper, the shape parameters, reliability and hazard rate functions of the inverted Kumaraswamy distribution are estimated using maximum likelihood and Bayesian methods based on dual generalized order statistics. The Bayes estimators are derived under the squared error loss function as a symmetric loss function and the linear-exponential loss function as an asymmetric loss function based on dual generalized order statistics. Confidence and credible intervals for the parameters, reliability and hazard rate functions are obtained. All results are specialized to lower record values, also a numerical study is presented to illustrate the theoretical procedures.
Highlights
The concept of generalized order statistics was introduced by Kamps (1995) as a unified models for ordered random variables which produce several models as a special case
The Bayes estimators are obtained under the squared error (SE) and linear exponential (LINEX) loss functions to estimate of the parameters, rf and hrf of the inverted Kumaraswamy (IKum) distribution based on dgos
The lower record values can be obtained as a special case from dgos by setting m = −1, k = 1; the estimation results obtained in Sections 2 and 3 can be specialized to lower records
Summary
The concept of generalized order statistics (gos) was introduced by Kamps (1995) as a unified models for ordered random variables which produce several models as a special case. The maximum likelihood (ML) and Bayes estimators, confidence intervals for the parameters, the reliability and the hazard rate functions of the IKum distribution based on Type II censored samples, are obtained. Fatima et al (2018) proposed the exponentiated IKum distribution; they derived some statistical properties of this distribution and used the ML method to estimate the parameters. Usman and ul Haq (2020) introduced the Marshall-Olkin extended IKum distribution, sub models were showed of this generalization They derived explicit expressions for major mathematical properties of this distribution and they estimated the parameters using the ML method.
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