On the Bayesian analysis of the mixture of Laplace distribution using the censored data under different loss functions

Article type: Research Article

Authors: Ali, Sajid^{a; b; *} | Aslam, Muhammad^b | Kazmi, Syed Mohsin Ali^c

Affiliations: [a] Department of Decision Sciences, Bocconi University, Milan, Italy | [b] Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan | [c] Sustainable Development Policy Institute, Islamabad, Pakistan

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: Constructing a flexible parametric classes of probability distributions appeared as a quite popular approach in Bayesian analysis for the last few decades. This study is planned in the same direction for two component Mixture of Laplace probability distribution considering heterogeneous population. We have considered censored and complete sample environments and derived the closed form expressions for the Bayes estimators and their posterior risks. In addition we have worked out complete sample expressions for the Maximum Likelihood (ML) estimates along with their Posterior Risk and constructed components of the information matrix. To examine the performance of these estimators we have evaluated their properties for different sample sizes, censoring rates, proportions of the component of mixture and a variety of loss functions. To highlight the practical significance we have included an illustrative application example based on a real-life mixture data.

Keywords: Information matrix, censored sampling, inverse transformation method, Squared Error Loss Function (SELF), Weighted Squared Error Loss Function (WSELF), Precautionary Loss Function, Modified Quadratic Squared Error Loss Function (M/QSELF), fixed test termination time, ML, non-informative prior, mixture distribution, posterior risk

DOI: 10.3233/MAS-2012-0227

Journal: Model Assisted Statistics and Applications, vol. 7, no. 3, pp. 209-227, 2012