Estimating Common Scale Parameter of Two Logistic Populations: A Bayesian Study

Abstract Estimation under equality restrictions is an age old problem and has been considered by several researchers in the past due to practical applications and theoretical challenges involved in it. Particularly, the problem has been extensively studied from classical as well as decision theoretic point of view when the underlying distribution is normal. In this paper, we consider the problem when the underlying distribution is non-normal, say, logistic. Specifically, estimation of the common scale parameter of two logistic populations has been considered when the location parameters are unknown. It is observed that closed forms of the maximum likelihood estimators (MLEs) for the associated parameters do not exist. Using certain numerical techniques the MLEs have been derived. The asymptotic confidence intervals have been derived numerically too, as these also depend on the MLEs. Approximate Bayes estimators are proposed using non-informative as well as conjugate priors with respect to the squared error (SE) and the LINEX loss functions. A simulation study has been conducted to evaluate the proposed estimators and compare their performances through mean squared error (MSE) and bias. Finally, two real life examples have been considered in order to show the potential applications of the proposed model and illustrate the method of estimation.