P. G. Sankaran

Quantile-Based Reliability Analysis

Quantile functions are equivalent alternatives to distribution functions in modeling and analysis of statistical data. The present article discusses the role of quantile functions in reliability studies. We present the hazard, mean residual, variance residual, and percentile residual quantile functions, their mutual relationships and expressions for the quantile functions in terms of these functions. Further, some theoretical results relating to the Hankin and Lee (2006) lambda distribution are discussed.

A bivariate pareto model and its applications to reliability

We consider a bivariate Pareto distribution, as a generalization of the Lindley-Singpurwalla model, by incorporating the influence of the operating conditions on a two-component dependent system. The properties of the model and its applications to reliability analysis are discussed.

Characterization of the Pearson family of distributions

The Pearson family of distributions is characterized in terms of the failure rates. Analogous results when failure time is discrete are presented. Theorems are proved which generalize some previously published results concerning the gamma and negative binomial distributions. >

Characterizations of Life Distributions Using Conditional Expectations of Doubly (Interval) Truncated Random Variables

In this article, we study reliability measures such as geometric vitality function and conditional Shannons measures of uncertainty proposed by Ebrahimi (1996) and Sankaran and Gupta (1999), respectively, for the doubly (interval) truncated random variables. In survival analysis and reliability engineering, these measures play a significant role in studying the various characteristics of a system/component when it fails between two time points. The interrelationships among these uncertainty measures for various distributions are derived and proved characterization theorems arising out of them.

Modelling lifetimes by quantile functions using Parzen's score function

The present paper introduces methods of constructing quantile functions as models of lifetimes with monotone and nonmonotone hazard functions. This is accomplished on the basis of the relationships the hazard quantile function has with the score function introduced by Parzen in connection with the tail heaviness of probability distributions. Three models illustrated here contain several existing models as particular cases. The appropriateness of the models in real situations is also demonstrated.

Some Characterization Results Based on Factorization of the (Reversed) Hazard Rate Function

Abstract In this article, the Fisher information is expressed in terms of the (reversed) hazard rate and several illustrated examples are given for its advantage. The concept is explored in the case of Type I and Type II censoring and characterization results are obtained for a class of distributions in which the (reversed) hazard rate factorizes into a function of the observation and a function of the parameter. Also, the Fisher information in the weighted models is studied with special emphasis on the exponential family of distributions. Finally, some concluding remarks are provided which help the practitioner to choose between the proposed procedure and the existing procedures.

Nonparametric estimation of hazard quantile function

In this paper, we study the estimation of the hazard quantile function based on right censored data. Two nonparametric estimators, one based on the empirical quantile density function and the other using the kernel smoothing method, are proposed. Asymptotic properties of the kernel-based estimator are discussed. Monte Carlo simulation studies are conducted to compare the two estimators. The method is illustrated for a real data set.

The Govindarajulu Distribution: Some Properties and Applications

In this article, we present various distributional properties and application to reliability analysis of the Govindarajulu distribution. A quantile-based analysis is performed as the distribution function is not analytically tractable. The properties of the distribution like percentiles, L-moments, L-skewness, and kurtosis and order statistics are presented. Various reliability characteristics are derived along with some characterization theorems by relationship between reliability measures. We also make a comparative study with other competing models with reference to real data.

Identification of models using failure rate and mean residual life of doubly truncated random variables

In this paper, we study the relationship between the failure rate and the mean residual life of doubly truncated random variables. Accordingly, we develop characterizations for exponential, Pareto II and beta distributions. Further, we generalize the identities for the Pearson and the exponential family of distributions given respectively in Nair and Sankaran (1991) and Consul (1995). Applications of these measures in the context of lengthbiased models are also explored.

Proportional Hazards Model for Multivariate Failure Time Data

Multivariate failure time data also referred to as correlated or clustered failure time data, often arise in survival studies when each study subject may experience multiple events. Statistical analysis of such data needs to account for intracluster dependence. In this article, we consider a bivariate proportional hazards model using vector hazard rate, in which the covariates under study have different effect on two components of the vector hazard rate function. Estimation of the parameters as well as base line hazard function are discussed. Properties of the estimators are investigated. We illustrated the method using two real life data. A simulation study is reported to assess the performance of the estimator.