Debasis Kundu

Indian Institute of Technology Kanpur | IIT Kanpur · Department of Mathematics and Statistics

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...

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 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 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...

Abstract Here, we address the problem of estimation of the parameters of a harmonic chirp model, often encountered in speech and music applications. This model was introduced recently by Christensen and Jensen [1] as an extension of a standard harmonic model. We propose two methods of estimation: the least squares estimation method and the approxim...

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...

The motivation of this paper came from a study which was conducted to examine the effect of laser treatment in delaying the onset of blindness in patients with diabetic retinopathy. The data are competing risks data with two dependent competing causes of failures, and there are ties. In this paper we have used the bivariate Weibull-geometric (BWG)...

Recently, Feizjavadian and Hashemi (Analysis of dependent competing risks in presence of progressive hybrid censoring using Marshall–Olkin bivariate Weibull distribution. Comput Stat Data Anal. 2015;82:19–34) provided a classical inference of a competing risks data set using Marshall–Olkin bivariate Weibull distribution when the failure of an unit...

Analysis of competing risks data plays an important role in the lifetime data analysis. Recently Feizjavadian and Hashemi (Computational Statistics and Data Analysis, vol. 82, 19-34, 2015) provided a classical inference of a competing risks data set using four-parameter Marshall-Olkin bivariate Weibull distribution when the failure of an unit at a...

In this article, we provide a consistent method of estimation for the parameters of a three-parameter generalized exponential distribution which avoids the problem of unbounded likelihood function. The method is based on a maximum likelihood estimation of the shape parameter, which uses location and scale invariant statistic, originally proposed by...

The Lehmann family of distributions includes Weibull, Gompertz, and Lomax models as special cases, all of which are quite useful for modeling lifetime data. Analyses of left truncated right censored data from the Lehmann family of distributions are carried out in this article. In particular, the special cases of Weibull, Gompertz, and Lomax distrib...

Chirp signals have played an important role in the statistical signal processing literature. An extensive amount of work has been done in analyzing different one dimensional chirp, two dimensional chirp and some related signal processing models. The main aim of this article is to introduce the challenges associated with these problems to the statis...

In real life, more often experimental units are susceptible to more than one risk factor. Moreover, some experimental units may not fail even if they are observed over a long period of time. In statistical analysis, competing risks models handle the first scenario while cure rate models have been introduced to analyze the long-term survivors in the...

Standard life testing experiments are not appropriate for testing highly reliable items as they often turn out to be time consuming and expensive under normal operating conditions. Under such scenario, accelerated life test (ALT) is often employed to obtain failure time data. In this paper, we consider a multi-step step-stress ALT (SSALT) model whe...

In this article, we mainly focus on the meta-analysis of several simple step-stress experimental data sets. It is assumed that independent data sets are obtained from s simple step-stress experiments. It is further assumed that the lifetime of the experimental units follow two parameter Weibull distribution with different shape and scale parameters...

In various capacities of statistical signal processing two-dimensional (2-D) chirp models have been considered significantly, particularly in image processing—to model gray-scale and texture images, magnetic resonance imaging, optical imaging etc. In this paper we address the problem of estimation of the unknown parameters of a 2-D chirp model unde...

In this article, we consider a flexible simple step-stress model for the Lehmann family of distributions, also known as the exponentiated distributions, when the data are Type-II censored. At each stress level, we assume that the lifetime distribution of the experimental units follows a member of the Lehmann family of distributions with different s...

The aim of this paper is to introduce an absolutely continuous bivariate inverse generalized exponential (BIGE) distribution. The proposed distribution has been obtained by removing the singular component from the BIGE distribution similarly as the Block and Basu absolute continuous bivariate exponential distribution. This distribution has four par...

In this paper, a decision-theoretic approach is used to obtain the Bayesian sampling plan (BSP) for the generalized Type-II hybrid censoring scheme when lifetimes of sampled units follow a one-parameter exponential distribution. An efficient loss function is used to decide whether to accept or reject the batch. The BSP is obtained by constructing t...

Professor C R Rao has made significant contributions in different areas of statistics and in related fields particularly in inference, biometrics, design of experiments, linear models, variance components, econometrics, and most of his contributions are well known to the statistical community. But it may not be known to many statisticians that Prof...

In statistical quality control, decision‐theoretic approach draws a significant amount of attention due to its economic considerations. In reliability life testing, decision‐theoretic approach has been used quite extensively under different censoring schemes. All these implementations are based on single sample of products coming from a particular...

Analyzing periodic or nearly periodic signals is a fundamental problem in Signal Processing. If the signal is periodic, then the sum of sinusoidal model has been used quite extensively to analyze the signal. But if the signal is nearly periodic, then si- nusoidal model may not be very effective. Different alternative models have been proposed in th...

In 2020, El-Morshedy et al. introduced a bivariate extension of the Burr type X generator (BBX-G) of distributions, and Muhammed presented a bivariate generalized inverted Kumaraswamy (BGIK) distribution. In this paper, we propose a more flexible generator of bivariate distributions based on the maximization process from an arbitrary three-dimensio...

Analyzing periodic or nearly periodic signals is a fundamental problem in Signal Processing. If the signal is periodic, then the sum of sinusoidal model has been used quite extensively to analyze the signal. But if the signal is nearly periodic, then si- nusoidal model may not be very effective. Different alternative models have been proposed in th...

The aim of this paper is to consider the bivariate inverse generalized exponential distribution which has a singular component. The bivariate inverse generalized exponential distribution can be used when the marginals have heavy tailed distributions, and they have non-monotone hazard functions. Due to presence of the singular component, it can be u...

In this chapter we have discussed seventeen different methods to estimate the parameters of sinusoidal model. Some of the methods are iterative and some are non-iterative in nature. Throughout this chapter it is assumed that the number of components is known. Estimation of the number of components will be discussed in Chap. 5. The main aim is to pr...

In this chapter, we have discussed different methods of estimating the number of components in a multiple sinusoidal model. This problem can be formulated as a model selection problem, hence any model selection procedure which is available in the literature can be used for this purpose. We have provided three different approaches namely (i) likelih...

In the last few chapters, we have discussed different aspects of the one-dimensional (1-D) sinusoidal frequency model. In this chapter, our aim is to introduce two dimensional (2-D) and three dimensional (3-D) frequency models, and discuss several issues related to them. The 2-D and 3-D sinusoidal frequency models are natural generalizations of the...

Chirp signals have played an important role in the statistical signal processing literature. An extensive amount of work has been done in analyzing different one dimensional chirp, two dimensional chirp and some related signal processing models. These models have been used in analyzing different real-life signals or images quite efficiently. It is...

The sinusoidal frequency model is a well-known model in different fields of science and technology and as has been observed in previous chapters, is a very useful model in explaining periodic or nearly periodical data. There are several other models which are practically some form of the multiple sinusoidal model, but also exploit some extra featur...

In this monograph, we have considered sinusoidal frequency model and many of its variants in one and higher dimensions. In all these models considered so far, amplitudes are assumed to be unknown constants. In this chapter, we allow the amplitudes to be random or some deterministic function of the index. Such random amplitude sinusoidal and chirp m...

This chapter provides a quick review of different concepts and results which have been used quite extensively throughout this monograph. Most of the results have been provided without proof, but references have been provided for interested readers. We have provided a brief review of (i) matrix theory, (ii) regression analysis, (iii) numerical algor...

In Chap. 3 we have discussed several estimators of the unknown parameters of a sinusoidal model. The theoretical properties of all the estimators discussed in Chap. 3, are not available in the literature. In this chapter we have provided the asymptotic properties of the estimators which ever are available in the literature. In most of the cases we...

In this chapter we have discussed the fundamental frequency model (FFM) and the generalized fundamental frequency model (GFFM). Both these models are special cases of the sinusoidal frequency model. But many real-life phenomena can be analyzed using such special models. In estimating unknown parameters of multiple sinusoidal model, there are severa...

In this chapter, we have provided the analyses of some real data sets using the models we have already discussed, namely, the multiple sinusoidal model, the fundamental frequency model, and the generalized fundamental frequency model. We have explicitly shown how different methods can be implemented in practice and for a given data set how to choos...

In this article, the analysis of left truncated and right censored competing risks data is carried out, under the assumption of the latent failure times model. It is assumed that there are two competing causes of failures, although most of the results can be extended for more than two causes of failures. The lifetimes corresponding to the competing...

In this article we consider the analysis of progressively censored competing risks data obtained from a simple step-stress experiment. It is assumed that there are only two competing causes of failures at each stress level and the lifetime distribution of each one of them is one parameter exponential distribution. Based on the cumulative exposure m...

Motivated by reliability systems whose components fail one by one and share a common load, this work provides a generalized Freund bivariate class of distributions for modeling the two component lifetimes of a parallel redundant system. When a component fails, such load-sharing systems can be repaired meanwhile the surviving one endures the total l...

In this paper, a multiple step-stress model is designed and analyzed when the data are Type-I censored. Lifetime distributions of the experimental units at each stress level are assumed to follow a two-parameter Weibull distribution. Further, distributions under each of the stress levels are connected through a tampered failure-rate based model. In...

Joint progressive censoring schemes are quite useful to conduct comparative life‐testing experiment of different competing products. Recently, Mondal and Kundu (“A New Two Sample Type‐II Progressive Censoring Scheme,” Commun Stat‐Theory Methods; 2018) introduced a joint progressive censoring scheme on two samples known as the balanced joint progres...

Progressive censoring schemes have received considerable attention recently. All of these developments are mainly based on a single population. Recently, Mondal and Kundu (2016 Mondal, S., & Kundu, D. (2016). A new two sample Type-II progressive censoring scheme. Retrieved from arXiv:1609.05805. doi:10.1080/03610926.2018.1472781[Taylor & Francis On...

This book introduces readers to various signal processing models that have been used in analyzing periodic data, and discusses the statistical and computational methods involved. Signal processing can broadly be considered to be the recovery of information from physical observations. The received signals are usually disturbed by thermal, electrical...