Estimation for Two-Parameter Generalized Exponential Distribution Based on Records

Abstract

This paper derives maximum likelihood estimators (MLEs) and some approximate MLEs (AMLEs) of unknown parameters of the generalized exponential distribution when data are lower record values. We derive approximate Bayes estimators through importance sampling and obtain corresponding Bayes predictive intervals for unknown parameters for lower record values from the generalized exponential distribution. For illustrative purposes, we examine the validity of the proposed estimation method by using real and simulated data.

Interval Estimation of the Stress-Strength Reliability for Lower Record Data Based on One-parameter Exponential Distribution Using Median Ranked Set Sampling and Record Ranked Set Sampling

“…Therefore, we can find the maximum likelihood estimator (MLE) of 𝑅 by substituting the MLEs of parameters � 1 and � 2 under the invariance property. The MLEs are found using the normal equation based on the lower records (Kang et al 2013):…”

Study on Cumulative Residual Entropy and Variance as Risk Measure

“…It should be noted that cumulative distribution function is more regular because it is defined as the integral form unlike the density function which is defined as the derivative of the probability distribution. The concept of CRE has found useful interpretations and applications in image alignment (Wang et al [8], Baratpoura[9], Hasan et al [10], Zhang and Li [11]), risk measure (Yang [12]), parameter estimation (Yang, [13]) and reliability (Asadi and Zohrevand [14]). In 2008, Drissi et al generalized CRE in Eq.…”

Investigation of Exponential Distribution Utilizing Randomly Censored Data under Balanced Loss Functions and Its Application to Clinical Data

“…Using several type-II censored samples, Kang et al [5] investigated entropy estimation for a double EXPD. When dealing with lower record values in the data, Kang et al [6] generated MLEs and approximations for the unknown parameters of the generalized EXPD. Chan et al [7] focused on type-II progressive hybrid censoring and statistical inference for the two-parameter EXPD.…”