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Sankaran Pg

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University of Cambridge

Μιχαήλ Τσαγρής

University of Crete

Durham University

Sevcan Demir Atalay

Ege University

Tomoyuki Ichiba

University of California, Santa Barbara

Hacettepe University

Mohamed I. Riffi

Islamic University of Gaza

Yogendra Chaubey

Concordia University (Canada)

The University Of Jordan

E.i.abdul Sathar

University of Kerala

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Papers by Sankaran Pg

The bilinear mean residual quantile function

Communications in Statistics - Theory and Methods, 2022

Nonparametric estimation of quantile-based entropy function

Communications in Statistics - Simulation and Computation, 2021

In this article, we propose three nonparametric estimators for quantile-based Shannon differentia... more

Correlations between biometrical characters in vanilla ( Vanilla planifolia Andrews)

Journal of Spices and Aromatic Crops, 2016

A study was undertaken to fmd out the extent of association among growth attributes of vanilla ( ... more A study was undertaken to fmd out the extent of association among growth attributes of vanilla ( Vanilla planifolia ) and to develop a model for determination of vine length based on biometrical observations. The characters, number of nodes, number of leaves and internodal length were significantly and positively correlated with vine length. The multiple regression equation derived exhibited a precision of 82.5 per cent.

Statistical Methods for Estimating Cure Fraction of COVID-19 Patients In India

The human race is under the COVID-19 pandemic menace since beginning of the year 2020. Even thoug... more The human race is under the COVID-19 pandemic menace since beginning of the year 2020. Even though the disease is easily transmissible, a massive fraction of the affected people are recovering. Most of the recovered patients will not experience death due to COVID-19, even if they observed for a long period. They can be treated as long term survivors (cured population) in the context of lifetime data analysis. In this article, we present some statistical methods to estimate the cure fraction of the COVID-19 patients in India. Proportional hazards mixture cure model is used to estimate the cure fraction and the effect of covariates gender and age on lifetime. The data available on website ‘https://api.cvoid19india.org’ is used in this study. We can see that, the cure fraction of the COVID-19 patients in India is more than 90%, which is indeed an optimistic information.

Modelling bivariate lifetime data using copula

METRON, 2018

Generally modelling lifetime data is carried out using probability distributions with the aid of ... more Generally modelling lifetime data is carried out using probability distributions with the aid of reliability functions such as hazard rate, mean residual life, etc. In the present work an alternative approach is proposed by considering bivariate copulas instead of bivariate distributions. We define the analogues of reliability functions that are expressed in terms of copulas and study their properties. The results of the study are applied to case of the copulas of a bivariate exponential family of distributions.

Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime

Metrika, 2018

Measure of uncertainty in past lifetime plays an important role in different areas such as inform... more Measure of uncertainty in past lifetime plays an important role in different areas such as information theory, reliability theory, survival analysis, economics, business, forensic science and other related fields. In this paper, we propose a cumulative Tsallis entropy in past lifetime based on quantile function. We obtain different characterizations based on the proposed measure and quantile-based reliability measures. We also study the quantile-based cumulative Tsallis entropy of order statistics in past lifetime.

Quantile-based cumulative Kullback–Leibler divergence

Statistics, 2017

The paper introduces a quantile-based cumulative Kullback-Leibler divergence and study its variou... more The paper introduces a quantile-based cumulative Kullback-Leibler divergence and study its various properties. Unlike the distribution function approach, the quantile-based measure possesses some unique properties. The quantile functions used in many applied works do not have any tractable distribution functions where the proposed measure is a useful tool to compute the distance between two random variables. Some useful bounds are obtained for quantile-based residual cumulative Kullback-Leibler divergence and quantile-based reliability measures. Characterization results based on the functional forms of quantile-based residual Kullback-Leibler divergence are obtained for some well-known life distributions, namely exponential, Pareto II and beta.

A martingale-based test for independence of time to failure and cause of failure for competing risks models

Communications in Statistics - Theory and Methods, 2016

In this article, we introduce a class of tests, using a martingale approach, for testing independ... more In this article, we introduce a class of tests, using a martingale approach, for testing independence of failure time and cause of failure for competing risks data. Asymptotic distribution of the proposed test statistic is derived. The procedure is illustrated with a real-life data. A simulation study is carried out to assess the level and power of the test.

Some Properties of Proportional Reversed Hazards Model Based on Quantile Functions

International Journal of Reliability, Quality and Safety Engineering, 2018

In this paper, we study some reliability aspects of proportional reversed hazards model (PRHM) us... more In this paper, we study some reliability aspects of proportional reversed hazards model (PRHM) using quantile functions and derive certain characteristic properties. A quantile-based relevation transform for past lifetime random variable is introduced. The relationships between quantile-based PRHM and quantile versions of measures of divergence are investigated.

Additive risks regression model for middle censored exponentiated-exponential lifetime data

Communications in Statistics - Simulation and Computation, 2017

introduced middle censoring which refers to data arising in situations where the exact lifetime b... more introduced middle censoring which refers to data arising in situations where the exact lifetime becomes unobservable if it falls within a random censoring interval. In the present paper we propose an additive risks regression model for a lifetime data subject to middle censoring, where the lifetimes are assumed to follow exponentiated exponential distribution. The regression parameters are estimated using the Expectation-Maximization algorithm. Asymptotic normality of the estimator is proposed. We report a simulation study to assess the finite sample properties of the estimator. We then analyze a real life data on survival times of larynx cancer patients studied by .

A proportional hazards model for the analysis of doubly censored competing risks data

Communications in Statistics - Theory and Methods, 2015

ABSTRACT Competing risks data are common in medical research in which lifetime of individuals can... more ABSTRACT Competing risks data are common in medical research in which lifetime of individuals can be classified in terms of causes of failure. In survival or reliability studies, it is common that the patients (objects) are subjected to both left censoring and right censoring, which is refereed as double censoring. The analysis of doubly censored competing risks data in presence of covariates is the objective of this study. We propose a proportional hazards model for the analysis of doubly censored competing risks data, using the hazard rate functions of Gray (1988), while focusing upon one major cause of failure. We derive estimators for regression parameter vector and cumulative baseline cause specific hazard rate function. Asymptotic properties of the estimators are discussed. A simulation study is conducted to assess the finite sample behavior of the proposed estimators. We illustrate the method using a real life doubly censored competing risks data.

Characterization of Lifetime Distributions Using Measure of Uncertainty

Calcutta Statistical Association Bulletin, 1999

In the present paper, we characterize exponential, Pareto, Wei bull and beta distributions using ... more In the present paper, we characterize exponential, Pareto, Wei bull and beta distributions using the concept of measure of uncertainty defined by Ebrahimi and Pellery (1995). Further, a new measure of uncertainty is introduced and its properties are discussed. Finally, we present a characterization theorem for extreme value distribution by extending the concept into negative set-up.

Quantile-based cumulative entropies

Communications in Statistics - Theory and Methods, 2016

ABSTRACT It is well known that Shannon’s entropy plays an important role in the measurement of un... more ABSTRACT It is well known that Shannon’s entropy plays an important role in the measurement of uncertainty of probability distributions. However, in certain situations Shannon entropy is not appropriate to measure the uncertainty and therefore an alternative measure has been introduced called cumulative residual entropy, based on the survival function (sf) instead of the probability density function (pdf) f(x) used in Shannon’s entropy. In the present paper, we introduce and study quantile versions of the cumulative entropy functions in the residual and past lifetimes. Unlike the cumulative entropies based on sf, the quantile-based cumulative entropy measures uniquely determine the underlying probability distribution.

A bivariate Pareto model

Statistics, 2012

Lindley-Singpurwalla (1986)'s bivariate Pareto distribution is one of the most popular bivariate ... more Lindley-Singpurwalla (1986)'s bivariate Pareto distribution is one of the most popular bivariate Pareto distribution. proposed a new bivariate Pareto distribution which also has Pareto marginals and it contains Lindley-Singpurwalla's bivariate Pareto model as a special case. It has several other interesting properties also. In this paper we re-visit Sankaran and Nair's bivariate Pareto model. We discuss several other new properties. The maximum likelihood estimators and two stage estimators are also investigated. We analyze two data sets for illustrative purposes. It is observed that this model can be used quite effectively to analyze competing risks data. Finally we propose some generalizations.

On bilinear hazard quantile functions

METRON, 2014

ABSTRACT In this paper, we introduce and study a class of distributions with bilinear hazard quan... more ABSTRACT In this paper, we introduce and study a class of distributions with bilinear hazard quantile function. Various distributional properties of the class of distributions are studied. We also discuss the reliability characteristics of the class of distributions. The estimators of the parameters of the class of distributions, using method of L-moments are derived. We apply the proposed class of distributions to a real data set.

Estimation and Modelling

Quantile-Based Reliability Analysis, 2013

Earlier in Chaps. 3 and 7, several types of models for lifetime data were discussed through their... more Earlier in Chaps. 3 and 7, several types of models for lifetime data were discussed through their quantile functions. These will be candidate distributions in specific situations. The selection of one of them or a new one is dictated by how well it can justify the data generating mechanisms and satisfy well other criteria like goodness of fit. Once the question of an initial choice of the model is resolved, the problem is then to test its adequacy against the observed data. This is accomplished by first estimating the parameters of the model and then carrying out a goodness-of-fit test. This chapter addresses the problem of estimation as well as some other modelling aspects.

Quantile Function Models

Quantile-Based Reliability Analysis, 2013

One of the objectives of quantile-based reliability analysis is to make use of quantile functions... more One of the objectives of quantile-based reliability analysis is to make use of quantile functions as models in lifetime data analysis. Accordingly, in this chapter, we discuss the characteristics of certain quantile functions known in the literature. The models considered are the generalized lambda distribution of Ramberg and Schmeiser, the generalized Tukey lambda family of Freimer, Kollia, Mudholkar and Lin, the four-parameter distribution of van Staden and Loots, the five-parameter lambda family and the power-Pareto model of Gilchrist, the Govindarajulu distribution and the generalized Weibull family of Mudholkar and Kollia.

Nonparametric estimators for a survivor function of paired recurrent events

Statistical Methodology, 2012

Quantile based stop-loss transform and its applications

Statistical Methods & Applications, 2012

Partial moments are extensively used in actuarial science for the analysis of risks. Since the fi... more Partial moments are extensively used in actuarial science for the analysis of risks. Since the first order partial moments provide the expected loss in a stop-loss treaty with infinite cover as a function of priority, it is referred as the stop-loss transform. In the present work, we discuss distributional and geometric properties of the first and second order partial moments defined in terms of quantile function. Relationships of the scaled stop-loss transform curve with the Lorenz, Gini, Bonferroni and Leinkuhler curves are developed.

Some new applications of the total time on test transforms

Statistical Methodology, 2013

The concept of total time on test transforms (TTT) is well known for its applications in differen... more The concept of total time on test transforms (TTT) is well known for its applications in different fields of scientific study. In this article we present four applications of TTT in reliability theory. First we characterize ageing criteria such as IFRA and NBU in terms of TTT. Then we utilize an iterated version to construct bathtub shaped hazard quantile functions and corresponding lifetime models. Further, an index is developed for numerically measuring the extent of IFR-ness of a life distribution. Finally we demonstrate how the distributional properties such as kurtosis and skewness can be derived from the TTT.

The bilinear mean residual quantile function

Communications in Statistics - Theory and Methods, 2022

Nonparametric estimation of quantile-based entropy function

Communications in Statistics - Simulation and Computation, 2021

In this article, we propose three nonparametric estimators for quantile-based Shannon differentia... more

Correlations between biometrical characters in vanilla ( Vanilla planifolia Andrews)

Journal of Spices and Aromatic Crops, 2016

A study was undertaken to fmd out the extent of association among growth attributes of vanilla ( ... more A study was undertaken to fmd out the extent of association among growth attributes of vanilla ( Vanilla planifolia ) and to develop a model for determination of vine length based on biometrical observations. The characters, number of nodes, number of leaves and internodal length were significantly and positively correlated with vine length. The multiple regression equation derived exhibited a precision of 82.5 per cent.

Statistical Methods for Estimating Cure Fraction of COVID-19 Patients In India

The human race is under the COVID-19 pandemic menace since beginning of the year 2020. Even thoug... more The human race is under the COVID-19 pandemic menace since beginning of the year 2020. Even though the disease is easily transmissible, a massive fraction of the affected people are recovering. Most of the recovered patients will not experience death due to COVID-19, even if they observed for a long period. They can be treated as long term survivors (cured population) in the context of lifetime data analysis. In this article, we present some statistical methods to estimate the cure fraction of the COVID-19 patients in India. Proportional hazards mixture cure model is used to estimate the cure fraction and the effect of covariates gender and age on lifetime. The data available on website ‘https://api.cvoid19india.org’ is used in this study. We can see that, the cure fraction of the COVID-19 patients in India is more than 90%, which is indeed an optimistic information.

Modelling bivariate lifetime data using copula

METRON, 2018

Generally modelling lifetime data is carried out using probability distributions with the aid of ... more Generally modelling lifetime data is carried out using probability distributions with the aid of reliability functions such as hazard rate, mean residual life, etc. In the present work an alternative approach is proposed by considering bivariate copulas instead of bivariate distributions. We define the analogues of reliability functions that are expressed in terms of copulas and study their properties. The results of the study are applied to case of the copulas of a bivariate exponential family of distributions.

Quantile-based reliability aspects of cumulative Tsallis entropy in past lifetime

Metrika, 2018

Measure of uncertainty in past lifetime plays an important role in different areas such as inform... more Measure of uncertainty in past lifetime plays an important role in different areas such as information theory, reliability theory, survival analysis, economics, business, forensic science and other related fields. In this paper, we propose a cumulative Tsallis entropy in past lifetime based on quantile function. We obtain different characterizations based on the proposed measure and quantile-based reliability measures. We also study the quantile-based cumulative Tsallis entropy of order statistics in past lifetime.

Quantile-based cumulative Kullback–Leibler divergence

Statistics, 2017

The paper introduces a quantile-based cumulative Kullback-Leibler divergence and study its variou... more The paper introduces a quantile-based cumulative Kullback-Leibler divergence and study its various properties. Unlike the distribution function approach, the quantile-based measure possesses some unique properties. The quantile functions used in many applied works do not have any tractable distribution functions where the proposed measure is a useful tool to compute the distance between two random variables. Some useful bounds are obtained for quantile-based residual cumulative Kullback-Leibler divergence and quantile-based reliability measures. Characterization results based on the functional forms of quantile-based residual Kullback-Leibler divergence are obtained for some well-known life distributions, namely exponential, Pareto II and beta.

A martingale-based test for independence of time to failure and cause of failure for competing risks models

Communications in Statistics - Theory and Methods, 2016

In this article, we introduce a class of tests, using a martingale approach, for testing independ... more In this article, we introduce a class of tests, using a martingale approach, for testing independence of failure time and cause of failure for competing risks data. Asymptotic distribution of the proposed test statistic is derived. The procedure is illustrated with a real-life data. A simulation study is carried out to assess the level and power of the test.

Some Properties of Proportional Reversed Hazards Model Based on Quantile Functions

International Journal of Reliability, Quality and Safety Engineering, 2018

In this paper, we study some reliability aspects of proportional reversed hazards model (PRHM) us... more In this paper, we study some reliability aspects of proportional reversed hazards model (PRHM) using quantile functions and derive certain characteristic properties. A quantile-based relevation transform for past lifetime random variable is introduced. The relationships between quantile-based PRHM and quantile versions of measures of divergence are investigated.

Additive risks regression model for middle censored exponentiated-exponential lifetime data

Communications in Statistics - Simulation and Computation, 2017

introduced middle censoring which refers to data arising in situations where the exact lifetime b... more introduced middle censoring which refers to data arising in situations where the exact lifetime becomes unobservable if it falls within a random censoring interval. In the present paper we propose an additive risks regression model for a lifetime data subject to middle censoring, where the lifetimes are assumed to follow exponentiated exponential distribution. The regression parameters are estimated using the Expectation-Maximization algorithm. Asymptotic normality of the estimator is proposed. We report a simulation study to assess the finite sample properties of the estimator. We then analyze a real life data on survival times of larynx cancer patients studied by .

A proportional hazards model for the analysis of doubly censored competing risks data

Communications in Statistics - Theory and Methods, 2015

ABSTRACT Competing risks data are common in medical research in which lifetime of individuals can... more ABSTRACT Competing risks data are common in medical research in which lifetime of individuals can be classified in terms of causes of failure. In survival or reliability studies, it is common that the patients (objects) are subjected to both left censoring and right censoring, which is refereed as double censoring. The analysis of doubly censored competing risks data in presence of covariates is the objective of this study. We propose a proportional hazards model for the analysis of doubly censored competing risks data, using the hazard rate functions of Gray (1988), while focusing upon one major cause of failure. We derive estimators for regression parameter vector and cumulative baseline cause specific hazard rate function. Asymptotic properties of the estimators are discussed. A simulation study is conducted to assess the finite sample behavior of the proposed estimators. We illustrate the method using a real life doubly censored competing risks data.

Characterization of Lifetime Distributions Using Measure of Uncertainty

Calcutta Statistical Association Bulletin, 1999

In the present paper, we characterize exponential, Pareto, Wei bull and beta distributions using ... more In the present paper, we characterize exponential, Pareto, Wei bull and beta distributions using the concept of measure of uncertainty defined by Ebrahimi and Pellery (1995). Further, a new measure of uncertainty is introduced and its properties are discussed. Finally, we present a characterization theorem for extreme value distribution by extending the concept into negative set-up.

Quantile-based cumulative entropies

Communications in Statistics - Theory and Methods, 2016

ABSTRACT It is well known that Shannon’s entropy plays an important role in the measurement of un... more ABSTRACT It is well known that Shannon’s entropy plays an important role in the measurement of uncertainty of probability distributions. However, in certain situations Shannon entropy is not appropriate to measure the uncertainty and therefore an alternative measure has been introduced called cumulative residual entropy, based on the survival function (sf) instead of the probability density function (pdf) f(x) used in Shannon’s entropy. In the present paper, we introduce and study quantile versions of the cumulative entropy functions in the residual and past lifetimes. Unlike the cumulative entropies based on sf, the quantile-based cumulative entropy measures uniquely determine the underlying probability distribution.

A bivariate Pareto model

Statistics, 2012

Lindley-Singpurwalla (1986)'s bivariate Pareto distribution is one of the most popular bivariate ... more Lindley-Singpurwalla (1986)'s bivariate Pareto distribution is one of the most popular bivariate Pareto distribution. proposed a new bivariate Pareto distribution which also has Pareto marginals and it contains Lindley-Singpurwalla's bivariate Pareto model as a special case. It has several other interesting properties also. In this paper we re-visit Sankaran and Nair's bivariate Pareto model. We discuss several other new properties. The maximum likelihood estimators and two stage estimators are also investigated. We analyze two data sets for illustrative purposes. It is observed that this model can be used quite effectively to analyze competing risks data. Finally we propose some generalizations.

On bilinear hazard quantile functions

METRON, 2014

ABSTRACT In this paper, we introduce and study a class of distributions with bilinear hazard quan... more ABSTRACT In this paper, we introduce and study a class of distributions with bilinear hazard quantile function. Various distributional properties of the class of distributions are studied. We also discuss the reliability characteristics of the class of distributions. The estimators of the parameters of the class of distributions, using method of L-moments are derived. We apply the proposed class of distributions to a real data set.

Estimation and Modelling

Quantile-Based Reliability Analysis, 2013

Earlier in Chaps. 3 and 7, several types of models for lifetime data were discussed through their... more Earlier in Chaps. 3 and 7, several types of models for lifetime data were discussed through their quantile functions. These will be candidate distributions in specific situations. The selection of one of them or a new one is dictated by how well it can justify the data generating mechanisms and satisfy well other criteria like goodness of fit. Once the question of an initial choice of the model is resolved, the problem is then to test its adequacy against the observed data. This is accomplished by first estimating the parameters of the model and then carrying out a goodness-of-fit test. This chapter addresses the problem of estimation as well as some other modelling aspects.

Quantile Function Models

Quantile-Based Reliability Analysis, 2013

One of the objectives of quantile-based reliability analysis is to make use of quantile functions... more One of the objectives of quantile-based reliability analysis is to make use of quantile functions as models in lifetime data analysis. Accordingly, in this chapter, we discuss the characteristics of certain quantile functions known in the literature. The models considered are the generalized lambda distribution of Ramberg and Schmeiser, the generalized Tukey lambda family of Freimer, Kollia, Mudholkar and Lin, the four-parameter distribution of van Staden and Loots, the five-parameter lambda family and the power-Pareto model of Gilchrist, the Govindarajulu distribution and the generalized Weibull family of Mudholkar and Kollia.

Nonparametric estimators for a survivor function of paired recurrent events

Statistical Methodology, 2012

Quantile based stop-loss transform and its applications

Statistical Methods & Applications, 2012

Partial moments are extensively used in actuarial science for the analysis of risks. Since the fi... more Partial moments are extensively used in actuarial science for the analysis of risks. Since the first order partial moments provide the expected loss in a stop-loss treaty with infinite cover as a function of priority, it is referred as the stop-loss transform. In the present work, we discuss distributional and geometric properties of the first and second order partial moments defined in terms of quantile function. Relationships of the scaled stop-loss transform curve with the Lorenz, Gini, Bonferroni and Leinkuhler curves are developed.

Some new applications of the total time on test transforms

Statistical Methodology, 2013

The concept of total time on test transforms (TTT) is well known for its applications in differen... more The concept of total time on test transforms (TTT) is well known for its applications in different fields of scientific study. In this article we present four applications of TTT in reliability theory. First we characterize ageing criteria such as IFRA and NBU in terms of TTT. Then we utilize an iterated version to construct bathtub shaped hazard quantile functions and corresponding lifetime models. Further, an index is developed for numerically measuring the extent of IFR-ness of a life distribution. Finally we demonstrate how the distributional properties such as kurtosis and skewness can be derived from the TTT.