Debasis Kundu

• Professor (Full) at Indian Institute of Technology Kanpur

In this manuscript we have proposed a modified Newton-Raphson algorithm to obtain efficient estimators of the elementary chirp signal parameters in presence of stationary noise. The asymptotic distribution of the least squares estimators which minimizes the residual sum of squares has been provided. The least squares optimization function is a high...

In this paper we have introduced a very flexible semi-parametric absolute continuous bivariate distribution based on proportional hazard class of distributions. Block and Basu’s bivariate exponential distribution is a member of this class. The key feature of the proposed class is that we do not assume any specific form of the base line distribution...

The paper deals with the estimation procedures for the proportional hazard class of distributions under a two‐sample balanced joint progressive censoring scheme. The baseline hazard function is assumed to be piecewise constant, instead of any specific form. This adds flexibility to the proposed model, and the shape of the underlying hazard function...

In this paper, we consider the estimation of the parameters of multiple component elementary chirp model based on weighted least squares estimators (WLSEs). Recently, Mittal et al. [17] proposed least squares estimators (LSEs) to estimate the parameters of the elementary chirp model. But it has been observed that LSEs are quite sensitive to outlier...

The generalized progressive censoring scheme has been considered one of the most general cases of censoring schemes. In this study, we consider two Weibull populations under a jointly generalized progressive hybrid censoring scheme as a more flexible extension of the exponential distribution. The methods presented in this paper let experimenters ev...

The generalized progressive censoring scheme has been considered one of the most general cases of censoring schemes. In this study, we consider two Weibull populations under a jointly generalized progressive hybrid censoring scheme as a more flexible extension of the exponential distribution. The methods presented in this paper let experimenters ev...

Recently, El-Bassiouny et al. [5] proposed the flexible Marshall-Olkin type bivariate modified Weibull distribution (BMWD) and obtained the maximum likelihood estimates (MLEs) of the five unknown parameters of the BMWD by solving five non-linear equations. The MLEs of parameters cannot be obtained in closed form. In this paper, we discuss about the...

The motivation of this work came when we were trying to analyze gold price data of the Indian market and the exchange rate data between Indian Rupees and US Dollars. It is observed that in both the cases there is a significant amount of time when \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepacka...

In many life-testing experiments, interest often lies in examining the effect of extreme or varying stress factors such as frequency, voltage, temperature, load etc. on the lifetimes of the experimental units. An experimenter often then performs the step-stress accelerated life testing (SSALT) experiment, a special case of the more general accelera...

In this article we consider the meta‐analysis of stage life testing experiments. We propose a method to combine the data obtained from s$s$ number of independent stage life testing experiments. We have assumed that there are only two stress levels for each stage life testing experiment and lifetime of the experimental units follows Weibull distribu...

Outlier-prone data sets are of immense interest in diverse areas including economics, finance, statistical physics, signal processing, telecommunications and so on. Stable laws (also known as α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs}...

Recently, El-Bassiouny et al. [5] proposed the flexible Marshall-Olkin type bivariate modified Weibull distribution (BMWD) and obtained the maximum likelihood estimates (MLEs) of the five unknown parameters of the BMWD by solving five non-linear equations. The MLEs of parameters cannot be obtained in closed form. In this paper, we discuss about the...

Real datasets exhibiting non-constant frequencies, can be analysed with the help of multi-component chirp signals adequately. This requires estimation of the number of chirp components in practice. The problem of estimation becomes difficult when the data is composed of moderate to large number of chirp components. We propose Bayesian approach to e...

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring (BJPC) scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale param...

This article presents the optimal Bayesian acceptance sampling plan (BASP) for two sample cases. In constructing the BASP, the decision-theoretic approach is used with a specified loss function, and the Bayes decision rule is developed by minimizing the Bayes risk. Both batches of products from the production line are accepted or rejected simultane...

The motivation of this work came when we were trying to analyze gold price data of the Indian market and the exchange rate data between Indian Rupees and US Dollars. It is observed that in both the cases there is a significant amount of time when X n = X n+1 , hence they cannot be ignored. In this paper we have introduced a very flexible discrete t...

In this paper, we have considered the classical and Bayesian inference of the unknown parameters of the lifetime distribution based on the observations obtained from a simple step‐stress life‐testing (SSLT) experiment and when more than one cause of failures are observed. We have used the Tampered Random Variable (TRV) approach. The main advantage...

The motivation of this paper came from two bivariate diabetic retinopathy data sets. The main aim is to test whether the laser treatment delays the onset of blindness compared to the traditional treatment. The first data set is of 197 patients and it provides the onset of blindness of the two eyes. The observed data are heavily censored on both the...

Left truncated right censored (LTRC) data arise quite commonly from survival studies. In this article, a model based on piecewise linear approximation is proposed for the analysis of LTRC data with covariates. Specifically, the model involves a piecewise linear approximation for the cumulative baseline hazard function of the proportional hazards mo...

Model misspecification can be a serious issue in any lifetime data analysis. Assumption of the correct model is very important particularly in prediction for future observations and for estimating the tail probabilities of any lifetime distribution. In this paper we have considered the model misspecification of the log-normal and Birnbaum-Saunders...

This paper introduces a parametric finite mixture model (FMM) approach to analyze the dependent competing risks data subjected to progressive first-failure censoring and multiple causes of failure. The cause-specific failure times are assumed to be flexibly modeled by the Lehmann family of distributions (also known as the exponentiated distribution...

Multi-component chirp signal models with equal chirp rates appear in various radar applications, e.g., synthetic aperture radar, echo signal of a rapid mobile target, etc. Many sub-optimal estimators have been developed for such models, however, these suffer from the problem of either identifiability or error propagation effect. In this paper, we h...

In this paper, we propose some estimation techniques to estimate the elementary chirp model parameters, which are encountered in sonar, radar, acoustics, and other areas. We derive asymptotic theoretical properties of least squares estimators and approximate least squares estimators for the one component elementary chirp model. It is proved that th...

In this paper we have proposed a novel robust method of estimation of the unknown parameters of a fundamental frequency and its harmonics model. Although the least squares estimators (LSEs) or the periodogram type estimators are the most efficient estimators, it is well known that they are not robust. In presence of outliers the LSEs are known to b...

In this paper we have considered the chirp like model which has been recently introduced, and it has a very close resemblance with a chirp model. We consider the weighted least squares estimators of the parameters of a chirp like model in presence of an additive stationary error, and study their properties. It is observed that although the least sq...

This paper presents a Bayesian acceptance sampling plan for simple step-stress life testing model, when the stress changing time is random, and the experimental units are subject to Type-II censoring. It is assumed that the lifetime distribution of the experimental item is exponential at each stress level with different scale parameters. We first p...

In this article, we consider the estimation of the three-parameter generalized exponential distribution. In presence of the unknown location parameter the usual maximum likelihood estimators do not exist for 0<α<1. The maximum product of spacings method serves as good alternative since it always exists and yields consistent estimators in the entire...

Chirp signal models and their generalizations have been used to model many natural and man-made phenomena in signal processing and time series literature. In recent times, several methods have been proposed for parameter estimation of these models. However, these methods are either statistically sub-optimal or computationally burdensome, especially...

The motivation of this paper came from two bivariate diabetic retinopathy data sets. The main aim is to test whether the laser treatment delays the onset of blindness compared to the traditional treatment. The first data set is of 197 patients and it provides the onset of blindness of the two eyes. The observed data are heavily censored on both the...

Recently, Kundu (2014, Sankhya, Ser. B, 167–189, 2014) proposed a geometric skew normal (GSN) distribution as an alternative to Azzalini’s skew normal (ASN) distribution. The GSN distribution can be a skewed distribution; it can be heavy tailed as well as multimodal also, unlike ASN distribution. It can be easily extended to the multivariate case a...

This paper discusses Bayesian sampling plan when the lifetime of the experimental units follows an exponential distribution and the data are generalized Type-I hybrid censored. Here, we adopt a decision-theoretic approach, and the Bayesian decision function is derived under a general loss function. Based on the Bayesian decision function, the Bayes...

In a life-testing experiment, the joint progressive censoring scheme for more than one exponential population was proposed by Rasouli and Balakrishnan (Commun Stat Theory Methods 39(12):2172–2191, 2010). In this paper, we focus on the joint adaptive progressive Type-II (JAPC-II) censoring scheme for two populations to reduce the experimental time a...

Multi-component chirp signal models with equal chirp rates appear in various radar applications, e.g., synthetic aperture radar, echo signal of a rapid mobile target, etc. Many sub-optimal estimators have been developed for such models, however, these suffer from the problem of either identifiability or error propagation effect. In this paper, we h...

In this study, in order to do a life testing experiment, sampled units are divided into a prefixed number of groups with equal number of units. Units in all the groups are tested simultaneously and independently and, in each group the experiment is terminated as soon as a prefixed time elapses or a prefixed number of failures occurs. We provide the...

In this article, we propose a failure rate based step‐stress accelerated life testing (SSALT) model assuming that the time‐to‐event distribution belongs to a fairly general family of distributions and the underlying population consists of long term survivors. With increase in stress levels, it is expected that the mean time to the event of interest...

Elementary chirp signals can be found in various fields of science and engineering. We propose two computationally efficient algorithms based on the choice of two different initial estimators to estimate the parameters of the elementary chirp model. It is observed that the proposed efficient estimators are consistent; they have the identical asympt...

In this article, we consider step-stress accelerated life testing (SSALT) models assuming that the time-to-event distribution belongs to the proportional hazard family and the underlying population consists of long-term survivors. Further, with an increase in stress levels, it is natural that the mean time to the event of interest gets shortened an...

In a progressively censored life testing experiment, the censored units can be used for some other life testing experiments. In a step-stress stage life testing experiment, we run parallel experiments while placing the progressively censored units at the higher stress level along with the main experiment. In this work, multiple step-stress stage li...

Estimation of parameters of the generalized inverse Lindley (GIL) distribution is considered under a hybrid censoring scheme. The point estimators, such as the maximum likelihood estimators using the Expectation-Maximization (E-M) algorithm, have been derived. The two approximate Bayes estimators using Tierney and Kadane’s method and Gibbs sampling...

There is a substantial amount of literature in the area of acceptance sampling plan with censored lifetime data. However, the optimality of a Bayesian sampling plan in the presence of competing risks has not been considered so far. In this paper, first, the Bayesian sampling plans (BSP) for Type-II and Type-I hybrid censoring schemes are discussed...

Finite mixing distributions often turn out as competent candidates to model time-to-event data possibly having multimodal structures. Such data is often available in case the event of interest occurs in presence of multiple modes. Although the finite mixed-Weibull model is a flexible model compared to single-population Weibull model, it has not wid...

In this paper, we propose some estimation techniques to estimate the elementary chirp model parameters, which are encountered in sonar, radar, acoustics, and other areas. We derive asymptotic theoretical properties of least squares estimators and approximate least squares estimators for the one-component elementary chirp model. It is proved that th...

Recently, the balanced joint progressive censoring (BJPC) for two samples has been introduced by the authors. This work comprises of developing testing of hypothesis for the BJPC scheme. An exact likelihood ratio test is developed to test the ratio of mean life times of two different products through joint life testing experiment. Along with this d...

Chirp signal models and their generalizations have been used to model many natural and man-made phenomena in signal processing and time series literature. In recent times, several methods have been proposed for parameter estimation of these models. These methods however are either statistically sub-optimal or computationally burdensome, specially f...

In this paper, we consider a two-dimensional random amplitude chirp signal model. It is assumed that the additive error is independent and identically distributed. This is an extension of the one dimensional random amplitude chirp model proposed by Besson et al. (IEEE Trans Signal Process 47(12):3208–3219, 1999) to two-dimension. The random amplitu...

The least squares method seems to be a natural choice in estimating the parameters of a chirp model. But the least squares estimators are very sensitive to the outliers. Even in presence of very few outliers, the performance of the least squares estimators becomes quite unsatisfactory. Due to this reason, the least absolute deviation method has bee...

In this paper, we study the problem of estimation of parameters of multichannel sinusoidal model. In multichannel sinusoidal model, the inherent frequencies from distinct channels are same with different amplitudes. It is assumed that the errors in individual channel are independently and identically distributed, whereas the signal from different c...

Model misspecification can be a serious issue in any lifetime data analysis. Assumption of the correct model is very important particularly in prediction for future observations and for estimating the tail probabilities of any lifetime distribution. In this paper we have considered the model misspecification of the log-normal and Birnbaum-Saunders...

In this paper we introduce a very general class of bivariate semi-parametric distributions whose marginals belong to the proportional hazard class, and it has a singular component. This model can be used quite effectively to analyze a bivariate data set when there are ties. Note that the Marshall-Olkin bivariate exponential distribution is a specia...

Copula models have attracted significant attention in the recent literature for modeling multivariate observations. An essential feature of copulas is that they enable us to specify the univariate marginal distributions and their joint behaviors separately. This paper provides asymptotic results for misspecification of copula models, and examines t...

The aim of this paper is twofold. First, the estimation of the Shannon and Rényi entropy measures of a generalized exponential distribution is discussed when data are progressively censored. The maximum-likelihood estimates are obtained. The Bayes estimates with respect to three loss functions are proposed. It is assumed that the unknown parameters...

In this paper, we obtain the stress-strength reliability estimation under balanced joint Type-II progressive censoring (BJPC) scheme for independent samples from two different populations. We simultaneously place two independent samples where the experimental units follow Weibull distributions with common shape parameter β and different scale param...

In this paper we introduce a discrete-time and continuous state-space Markov stationary process {Xn;n=1,2,…}, where Xn has a two-parameter Weibull distribution, Xn's are dependent and there is a positive probability that Xn=Xn+1. The motivation came from the gold price data where there are several instances for which Xn=Xn+1. Hence, the existing me...

Under adaptive progressive Type-II censoring schemes, order restricted inference based on competing risks data is discussed in this article. The latent failure lifetimes for the competing causes are assumed to follow Weibull distributions, with an order restriction on the scale parameters of the distributions. The practical implication of this orde...

The generalized progressive hybrid censoring schemes (GPHCS) have become quite popular in the case when there are very few failures before pre-determined time T in progressive hybrid censoring schemes. Whereas the GPHCS always ensures a fixed number of failures, which makes this scheme very popular. In this paper, we introduce a new joint generaliz...

In this paper, we propose a method based on maximizing a periodogram-type function for parameter estimation of a two-dimensional (2-D) mono-component chirp signal model. The obtained estimators are called approximate least squares estimators (ALSEs). We also put forward a sequential algorithm for parameter estimation of a more general version of th...

In a life testing experiment, the successive failure times at putting n units under test are recorded under consideration that the advance xed experiment is terminated at time T. is type of censoring scheme, called conventional Type-I censoring scheme, is used widely. In this paper, we assume that the items' failure times are independent and distri...

In this paper, we develop statistical inference of competing risks samples which are collected under a joint Type-II censoring scheme of products with Weibull lifetime distributions. These inferences are drawn from two independent fatal risks and come from two different lines of production with the same facility. The model parameters and the parame...

In this paper we study the problem of estimating unknown parameters of a two-parameter distribution with bathtub shape under the assumption that data are type I progressive hybrid censored. We derive maximum likelihood estimators and then obtain the observed Fisher information matrix. Bayes estimators are also obtained under the squared error loss...

In this paper a new bivariate lifetime distribution is introduced. Its marginal distribution functions follow two-parameter Chen distribution, which has a bathtub shaped or increasing hazard rate functions. The proposed distribution, which we call a bivariate Chen distribution (BCD), is of Marshall-Olkin type and it is a singular distribution. Seve...

In this paper, we propose a computationally faster yet conceptually simple methodology to estimate the parameters of a two-dimensional (2-D) sinusoidal model in the presence of additive white noise. We develop the large sample properties like consistency and asymptotic normality of these low-complexity estimators, and they are observed to be theore...

In this paper, a quantum scheme for a two-qubit system (2QS) and field initially prepared in the excited negative binomial distribution is presented. The field photon statistics is detected from the evolution of the Mandel parameter, while the evolution of von Neumann entropy detects the nonlocal correlation between the 2QS and radiation field. The...

In this paper, we introduce a new joint adaptive Type-II progressive censoring (JAPC) scheme for independent samples from two different populations. We place two independent samples simultaneously on a life testing experiment. It is assumed that the lifetime of the experimental units of the populations follow exponential distribution with mean θ 1...

In this paper we introduce a new discrete time and continuous state space stationary process {Xn;n = 1,2,…}, such that Xn follows a two-parameter generalized exponential (GE) distribution. Joint distribution functions, characterization and some dependency properties of this new process have been investigated. The GE-process has three unknown parame...

Log-normal, Weibull, and log-logistic distributions are widely used in modeling nonnegative skewed data. We develop sequential methodologies to discriminate between any two of these three distributions as well as to discriminate among these three distributions. These methods are extended to discriminate M(≥2) distributions from location-scale, log-...

Sinusoidal model and chirp model are the two fundamental models in digital signal processing. Recently, a chirp-like model was introduced by Grover et al. (International conference on computing, power and communication technologies, IEEE, pp. 1095–1100, 2018). A chirp-like model is a generalization of a sinusoidal model and provides an alternative...

In this paper we introduce a new discrete time and continuous state space stationary process $\{X_n; n = 1, 2, \ldots \}$, such that $X_n$ follows a two-parameter generalized exponential (GE) distribution. Joint distribution functions, characterization and some dependency properties of this new process have been investigated. The GE-process has thr...

The main aim of this paper is to introduce a new family of distributions, namely compound zero-truncated Poisson exponential distribution of which exponential distribution is a special case. The proposed family of distributions represents the zero truncated-Poisson sum of independent and identically distributed exponential random variables. The pro...

The Bayesian sampling plan for two parameter exponential distribution has been considered by Lam (1990) under the conventional Type-II censoring. Lin et al. (2008b) have obtained an exact Bayesian sampling plan for one parameter exponential distribution under Type-I and Type-II hybrid censoring schemes. In this paper, we obtain an optimal Bayesian...

In this article, the authors provide a glimpse into the legendary career of centenarian Professor C. Radhakrishna Rao, a career that is inextricably linked to the history of modern statistics from Pearson and Fisher to the age of big data and Artificial Intelligence. A scientist of extraordinary vision, his ground‐breaking contributions have influe...

In this paper, we consider the estimation of the unknown parameters of the multiple chirp signal model in presence of additive error. The chirp signals are quite common in many areas of science and engineering, specially sonar, radar, audio signals etc. The observed signals are usually corrupted by noise. In di�erent signal processing applications...

Parametric modelling of physical phenomena has received a great deal of attention in the signal processing literature. Different models like ARMA models, sinusoidal models, harmonic models, models with amplitude modulation, models with frequency modulation and their different versions and combinations have been used to describe natural and syntheti...