It has become increasingly common in epidemiological studies to pool specimens across subjects as... more It has become increasingly common in epidemiological studies to pool specimens across subjects as a useful cot-cutting technique to achieve accurate quantification of biomarkers and certain environmental chemicals. The data collected from these pooled samples can then be utilized to estimate the Youden Index, which measures biomarker's effectiveness and aids in the selection of an optimal threshold value, as a summary measure of the Receiver Operating Characteristic curve. The aim of this paper is to make use of generalized approach to estimate and testing of the Youden index. This goal is accomplished by the comparison of classical and generalized procedures for the Youden Index with the aid of pooled samples from the shifted-exponentially distributed biomarkers for the low-risk and high-risk patients. These are juxtaposed using confidence intervals, p-values, power of the test, size of the test, and coverage probability with a wide-ranging simulation study featuring a selection of various scenarios. In order to demonstrate the advantages of the proposed generalized procedures over its classical counterpart, an illustrative example is discussed using the Duchenne Muscular Dystrophy data available at http://biostat.mc.vanderbilt.edu/wiki/Main/DataSets or http://lib.stat.cmu.edu/datasets/.
Inthispaper, weconsider thelong-run availabilityofa seriessystem having several independent renew... more Inthispaper, weconsider thelong-run availabilityofa seriessystem having several independent renewable components with Pareto distributed failure and repair times. We are interested in hypothesis testing and interval estimation of the availability of the system. For this problem, there are no exact or approximate tests or confidence intervals available in literature. Generalized test and a generalized confidence interval based on the generalized variable method are given. An example using the limited simulation study is given to illustrate and to demonstrate the advantages of the proposed generalized variable method over the approximate method.
Abstract Consider k random samples which are independently drawn from k shifted-exponential distr... more Abstract Consider k random samples which are independently drawn from k shifted-exponential distributions, with respective scale parameters σ 1 , σ 2 , … , σ k and common location parameter θ . On the basis of the given samples and in a Bayesian framework, we address the problem of point and interval estimation of the location parameter θ under the conjugate priors, which are usually proper priors. Moreover, we also address the problem of testing the equality of the location parameters. We propose Bayesian hypothesis testing procedures for the equality of the location parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Our proposed Bayesian procedures are compared and contrasted, via a comparison study, a simulation study, and a real-world data analysis, to the existing classical exact procedures proposed by Tippett (Tippett’s method (Tippett, 1931)), Fisher (Fisher’s method (Fisher, 1932)), Stouffer (Inverse normal method (Stouffer et al., 1949)), and George (Logit method (George, 1977)), and to the generalized variable procedures proposed by Tsui and Weerahandi (Generalized p-value method (Tsui and Weerahandi, 1989)).
Abstract The problem of hypothesis testing and interval estimation, based on the generalized vari... more Abstract The problem of hypothesis testing and interval estimation, based on the generalized variable method, for the reliability function of Pareto distribution using progressively type II censored data with fixed removals are considered. The confidence limits and testing procedures have to be numerically obtained; however, the required computations are simple and straightforward. There are no exact or approximate testing procedures and confidence intervals for reliability parameter of a Pareto distribution based on the progressively type-II right censored data with random or fixed removals available in the literature. In addition, generalized coverage probabilities, generalized size of the test, and adjusted and unadjusted generalized powers of the test are also discussed. Comparison of the reliability function under the classical paradigm and the generalized paradigm is done citing an illustrative example and an example based on the simulated data to demonstrate the advantages and merits of the proposed generalized variable method over the classical method.
ABSTRACT Under a two-parameter exponential distribution, this study constructs the generalized lo... more ABSTRACT Under a two-parameter exponential distribution, this study constructs the generalized lower confidence limit of the lifetime performance index CL based on type-II right-censored data. The confidence limit has to be numerically obtained; however, the required computations are simple and straightforward. Confidence limits of CL computed under the generalized paradigm are compared with those of CL computed under the classical paradigm, citing an illustrative example with real data and two examples with simulated data, to demonstrate the merits and advantages of the proposed generalized variable method over the classical method.
ABSTRACT In this study, we discuss the classical, Bayesian, and generalized inference of the reli... more ABSTRACT In this study, we discuss the classical, Bayesian, and generalized inference of the reliability parameter At least s of the exceed of an s-out-of-k:G system with strength components subjected to a common stress Y whose probability densities are independent two-parameter general class of exponentiated inverted exponential distributions. These statistical analyses are carried out based on the progressively type-II right censored data with uniformly random removals. Under squared error and LINEX loss functions, Bayes estimates are developed by using Lindley's approximation and the Markov Chain Monte Carlo method due to the lack of closed forms of the posterior distributions. Generalized inferences are performed based on the generalized variable method. Simulation studies and real-world data analyses are given to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected confidence lengths of the confidence interval, and biases of the estimator are also discussed. Comparison and contrast among the classical, Bayesian, and generalized inferences of the reliability parameter in the multicomponent stress-strength model are performed.
The inference about the reliability function of Burr XII distribution using the concept of genera... more The inference about the reliability function of Burr XII distribution using the concept of generalized variable method based on progressively type II censoring with random removals, where the number of units removed at each failure time has a discrete uniform distribution, is proposed. As assessed by simulation, the coverage probabilities of the proposed approach are found to be very close to the nominal level even for small samples. The proposed new approaches are computationally simple and are easy to use. The method is illustrated using two examples.
American Journal of Mathematical and Management Sciences, 2016
SYNOPTIC ABSTRACT Within both the common- and private-value paradigms, statistical inferences for... more SYNOPTIC ABSTRACT Within both the common- and private-value paradigms, statistical inferences for the expected winning bids are considered. Under the common-value setting, Weibull and normal distributions are considered for modeling the cost estimates whereas Weibull, Pareto, and exponential distributions are considered under the private-value setting. Using the recently introduced Generalized Variable Method (GVM), we propose generalized tests and generalized confidence intervals for the expected winning bids for risk-neutral sealed-bid auctions with common- and private-value bidders under various bidders’ cost-estimate distributions. A simulation study is described to illustrate the proposed procedures.
Communications in Statistics - Theory and Methods, 2016
ABSTRACT This article deals with the problem of Bayesian inference concerning the common scale pa... more ABSTRACT This article deals with the problem of Bayesian inference concerning the common scale parameter of several Pareto distributions. Bayesian hypothesis testing of, and Bayesian interval estimation for, the common scale parameter is given. Numerical studies including a comparison study, a simulation study, and a practical application study are given in order to illustrate our procedures and to demonstrate the performance, advantages, and merits of the Bayesian procedures over the classical and generalized variable procedures.
Communications in Statistics - Simulation and Computation, 2015
ABSTRACT The Theil, Pietra, Éltetö and Frigyes measures of income inequality associated with the ... more ABSTRACT The Theil, Pietra, Éltetö and Frigyes measures of income inequality associated with the Pareto distribution function are expressed in terms of parameters defining the Pareto distribution. Inference procedures based on the generalized variable method, the large sample method, and the Bayesian method for testing of, and constructing confidence interval for, these measures are discussed. The results of Monte Carlo study are used to compare the performance of the suggested inference procedures from a population characterized by a Pareto distribution.
Communications in Statistics - Theory and Methods, 2015
Abstract In this article, Bayesian inference for the Offered Optical Network Unit Load (OOL) usin... more Abstract In this article, Bayesian inference for the Offered Optical Network Unit Load (OOL) using non-informative, gamma, power function, and gamma-power function priors is considered. Pareto distributed ON-and OFF-periods generated by the ON/OFF sources at an Optical Network Unit (ONU) in an Ethernet Passive Optical Network (EPON) system are assumed for our implementation in this article. A simulation study and a real-data-based illustrative example are given to demonstrate the advantages of the proposed Bayesian method over the large-sample method.
A two-factor fixed-effect unbalanced additive model without the assumption of equal variances is ... more A two-factor fixed-effect unbalanced additive model without the assumption of equal variances is considered. By taking the generalized p-value approach, the classical F-test for the main effects of the unbalanced additive model is extended to the case of unequal error variances. This generalized F-test can be utilized in significance testing or in fixed level testing under the Neyman-Pearson theory. This non-trivial extension is similar to the generalized F-test for the two-way ANOVA model under heteroscedasticity. Examples are cited to illustrate the proposed test and to demonstrate the significance and verification of this new model that are worthwhile to resort to a numerically extensive testing procedure when the problem of heteroscedasticity is serious or the assumption of homoscedasticity is not reasonable in additive models.
A problem of interest in this paper is statistical inferences concerning the common shape paramet... more A problem of interest in this paper is statistical inferences concerning the common shape parameter of several Pareto distributions. Using the generalized variable approach, generalized confidence intervals and generalized tests for testing the common shape parameter are given. An example is given in order to illustrate our procedures. A limited simulation study is given to demonstrate the performance of the proposed procedures.
The problem of hypothesis testing and interval estimation based on the generalized variable metho... more The problem of hypothesis testing and interval estimation based on the generalized variable method of the reliability parameter or the probability $$ R=\Pr (X>Y)$$R=Pr(X>Y) of an item of strength $$X$$X subject to a stress $$Y$$Y when $$X$$X and $$Y$$Y are independent two-parameter Pareto distributed random variables is given. We discuss the use of p value as a basis for hypothesis testing. There are no exact or approximate testing procedures and confidence intervals for reliability parameter for two-parameter Pareto stress–strength model available in the literature. A simulation study is given to illustrate the proposed generalized variable method. The generalized size, generalized adjusted and unadjusted powers of the test, generalized coverage probabilities are also discussed by comparing with their classical counterparts.
The Weibull distribution, frequently used for life data analysis, is composited with inverse Weib... more The Weibull distribution, frequently used for life data analysis, is composited with inverse Weibull distribution to obtain a computationally convenient parametric distribution for modeling reliability data. This two-parameter smooth and continuous natural composition has an inverse Weibull density up to an unknown threshold value and Weibull density for the remainder. The resulting density is similar in shape to the inverse Weibull density, yet its upper tail is lighter than the Weibull density. And, the right-tail behavior is quite similar to the Weibull density. The least squares parameter estimation technique is discussed by analyzing a repair time reliability data.
Physical measurements like dimensions, including time, and angles in scientific experiments are f... more Physical measurements like dimensions, including time, and angles in scientific experiments are frequently recorded without their algebraic sign. The directions of those physical quantities measured with respect to a frame of reference in most practical applications are considered to be unimportant and are ignored. As a consequence, the underlying distribution of measurements is replaced by a distribution of absolute measurements. When the underlying distribution is logistic, the resulting distribution is called the “folded logistic distribution”. Here, the properties of the folded logistic distribution will be presented and the techniques for estimating parameters will be given. The advantages of using this folded logistic distribution over the folded normal distribution will be discussed and some examples will be cited.
Journal of Statistical Computation and Simulation, 2014
This paper considers the development of inferential techniques based on the generalized variable ... more This paper considers the development of inferential techniques based on the generalized variable method (GV-Method) for the location parameter of the general half-normal distribution. We are interested in hypothesis testing of, and interval estimation for, the location parameter. Body fat data, urinary excretion rate data, and simulated data are used to illustrate the application and to demonstrate the advantages of the proposed GV-Method over the large-sample method and the Bayesian method.
It has become increasingly common in epidemiological studies to pool specimens across subjects as... more It has become increasingly common in epidemiological studies to pool specimens across subjects as a useful cot-cutting technique to achieve accurate quantification of biomarkers and certain environmental chemicals. The data collected from these pooled samples can then be utilized to estimate the Youden Index, which measures biomarker's effectiveness and aids in the selection of an optimal threshold value, as a summary measure of the Receiver Operating Characteristic curve. The aim of this paper is to make use of generalized approach to estimate and testing of the Youden index. This goal is accomplished by the comparison of classical and generalized procedures for the Youden Index with the aid of pooled samples from the shifted-exponentially distributed biomarkers for the low-risk and high-risk patients. These are juxtaposed using confidence intervals, p-values, power of the test, size of the test, and coverage probability with a wide-ranging simulation study featuring a selection of various scenarios. In order to demonstrate the advantages of the proposed generalized procedures over its classical counterpart, an illustrative example is discussed using the Duchenne Muscular Dystrophy data available at http://biostat.mc.vanderbilt.edu/wiki/Main/DataSets or http://lib.stat.cmu.edu/datasets/.
Inthispaper, weconsider thelong-run availabilityofa seriessystem having several independent renew... more Inthispaper, weconsider thelong-run availabilityofa seriessystem having several independent renewable components with Pareto distributed failure and repair times. We are interested in hypothesis testing and interval estimation of the availability of the system. For this problem, there are no exact or approximate tests or confidence intervals available in literature. Generalized test and a generalized confidence interval based on the generalized variable method are given. An example using the limited simulation study is given to illustrate and to demonstrate the advantages of the proposed generalized variable method over the approximate method.
Abstract Consider k random samples which are independently drawn from k shifted-exponential distr... more Abstract Consider k random samples which are independently drawn from k shifted-exponential distributions, with respective scale parameters σ 1 , σ 2 , … , σ k and common location parameter θ . On the basis of the given samples and in a Bayesian framework, we address the problem of point and interval estimation of the location parameter θ under the conjugate priors, which are usually proper priors. Moreover, we also address the problem of testing the equality of the location parameters. We propose Bayesian hypothesis testing procedures for the equality of the location parameters under the noninformative prior. The noninformative prior is usually improper which yields a calibration problem that makes the Bayes factor to be defined up to a multiplicative constant. So we propose the default Bayesian hypothesis testing procedures based on the fractional Bayes factor and the intrinsic Bayes factors under the reference priors. Our proposed Bayesian procedures are compared and contrasted, via a comparison study, a simulation study, and a real-world data analysis, to the existing classical exact procedures proposed by Tippett (Tippett’s method (Tippett, 1931)), Fisher (Fisher’s method (Fisher, 1932)), Stouffer (Inverse normal method (Stouffer et al., 1949)), and George (Logit method (George, 1977)), and to the generalized variable procedures proposed by Tsui and Weerahandi (Generalized p-value method (Tsui and Weerahandi, 1989)).
Abstract The problem of hypothesis testing and interval estimation, based on the generalized vari... more Abstract The problem of hypothesis testing and interval estimation, based on the generalized variable method, for the reliability function of Pareto distribution using progressively type II censored data with fixed removals are considered. The confidence limits and testing procedures have to be numerically obtained; however, the required computations are simple and straightforward. There are no exact or approximate testing procedures and confidence intervals for reliability parameter of a Pareto distribution based on the progressively type-II right censored data with random or fixed removals available in the literature. In addition, generalized coverage probabilities, generalized size of the test, and adjusted and unadjusted generalized powers of the test are also discussed. Comparison of the reliability function under the classical paradigm and the generalized paradigm is done citing an illustrative example and an example based on the simulated data to demonstrate the advantages and merits of the proposed generalized variable method over the classical method.
ABSTRACT Under a two-parameter exponential distribution, this study constructs the generalized lo... more ABSTRACT Under a two-parameter exponential distribution, this study constructs the generalized lower confidence limit of the lifetime performance index CL based on type-II right-censored data. The confidence limit has to be numerically obtained; however, the required computations are simple and straightforward. Confidence limits of CL computed under the generalized paradigm are compared with those of CL computed under the classical paradigm, citing an illustrative example with real data and two examples with simulated data, to demonstrate the merits and advantages of the proposed generalized variable method over the classical method.
ABSTRACT In this study, we discuss the classical, Bayesian, and generalized inference of the reli... more ABSTRACT In this study, we discuss the classical, Bayesian, and generalized inference of the reliability parameter At least s of the exceed of an s-out-of-k:G system with strength components subjected to a common stress Y whose probability densities are independent two-parameter general class of exponentiated inverted exponential distributions. These statistical analyses are carried out based on the progressively type-II right censored data with uniformly random removals. Under squared error and LINEX loss functions, Bayes estimates are developed by using Lindley's approximation and the Markov Chain Monte Carlo method due to the lack of closed forms of the posterior distributions. Generalized inferences are performed based on the generalized variable method. Simulation studies and real-world data analyses are given to illustrate the proposed procedures. The size of the test, adjusted and unadjusted power of the test, coverage probability and expected confidence lengths of the confidence interval, and biases of the estimator are also discussed. Comparison and contrast among the classical, Bayesian, and generalized inferences of the reliability parameter in the multicomponent stress-strength model are performed.
The inference about the reliability function of Burr XII distribution using the concept of genera... more The inference about the reliability function of Burr XII distribution using the concept of generalized variable method based on progressively type II censoring with random removals, where the number of units removed at each failure time has a discrete uniform distribution, is proposed. As assessed by simulation, the coverage probabilities of the proposed approach are found to be very close to the nominal level even for small samples. The proposed new approaches are computationally simple and are easy to use. The method is illustrated using two examples.
American Journal of Mathematical and Management Sciences, 2016
SYNOPTIC ABSTRACT Within both the common- and private-value paradigms, statistical inferences for... more SYNOPTIC ABSTRACT Within both the common- and private-value paradigms, statistical inferences for the expected winning bids are considered. Under the common-value setting, Weibull and normal distributions are considered for modeling the cost estimates whereas Weibull, Pareto, and exponential distributions are considered under the private-value setting. Using the recently introduced Generalized Variable Method (GVM), we propose generalized tests and generalized confidence intervals for the expected winning bids for risk-neutral sealed-bid auctions with common- and private-value bidders under various bidders’ cost-estimate distributions. A simulation study is described to illustrate the proposed procedures.
Communications in Statistics - Theory and Methods, 2016
ABSTRACT This article deals with the problem of Bayesian inference concerning the common scale pa... more ABSTRACT This article deals with the problem of Bayesian inference concerning the common scale parameter of several Pareto distributions. Bayesian hypothesis testing of, and Bayesian interval estimation for, the common scale parameter is given. Numerical studies including a comparison study, a simulation study, and a practical application study are given in order to illustrate our procedures and to demonstrate the performance, advantages, and merits of the Bayesian procedures over the classical and generalized variable procedures.
Communications in Statistics - Simulation and Computation, 2015
ABSTRACT The Theil, Pietra, Éltetö and Frigyes measures of income inequality associated with the ... more ABSTRACT The Theil, Pietra, Éltetö and Frigyes measures of income inequality associated with the Pareto distribution function are expressed in terms of parameters defining the Pareto distribution. Inference procedures based on the generalized variable method, the large sample method, and the Bayesian method for testing of, and constructing confidence interval for, these measures are discussed. The results of Monte Carlo study are used to compare the performance of the suggested inference procedures from a population characterized by a Pareto distribution.
Communications in Statistics - Theory and Methods, 2015
Abstract In this article, Bayesian inference for the Offered Optical Network Unit Load (OOL) usin... more Abstract In this article, Bayesian inference for the Offered Optical Network Unit Load (OOL) using non-informative, gamma, power function, and gamma-power function priors is considered. Pareto distributed ON-and OFF-periods generated by the ON/OFF sources at an Optical Network Unit (ONU) in an Ethernet Passive Optical Network (EPON) system are assumed for our implementation in this article. A simulation study and a real-data-based illustrative example are given to demonstrate the advantages of the proposed Bayesian method over the large-sample method.
A two-factor fixed-effect unbalanced additive model without the assumption of equal variances is ... more A two-factor fixed-effect unbalanced additive model without the assumption of equal variances is considered. By taking the generalized p-value approach, the classical F-test for the main effects of the unbalanced additive model is extended to the case of unequal error variances. This generalized F-test can be utilized in significance testing or in fixed level testing under the Neyman-Pearson theory. This non-trivial extension is similar to the generalized F-test for the two-way ANOVA model under heteroscedasticity. Examples are cited to illustrate the proposed test and to demonstrate the significance and verification of this new model that are worthwhile to resort to a numerically extensive testing procedure when the problem of heteroscedasticity is serious or the assumption of homoscedasticity is not reasonable in additive models.
A problem of interest in this paper is statistical inferences concerning the common shape paramet... more A problem of interest in this paper is statistical inferences concerning the common shape parameter of several Pareto distributions. Using the generalized variable approach, generalized confidence intervals and generalized tests for testing the common shape parameter are given. An example is given in order to illustrate our procedures. A limited simulation study is given to demonstrate the performance of the proposed procedures.
The problem of hypothesis testing and interval estimation based on the generalized variable metho... more The problem of hypothesis testing and interval estimation based on the generalized variable method of the reliability parameter or the probability $$ R=\Pr (X>Y)$$R=Pr(X>Y) of an item of strength $$X$$X subject to a stress $$Y$$Y when $$X$$X and $$Y$$Y are independent two-parameter Pareto distributed random variables is given. We discuss the use of p value as a basis for hypothesis testing. There are no exact or approximate testing procedures and confidence intervals for reliability parameter for two-parameter Pareto stress–strength model available in the literature. A simulation study is given to illustrate the proposed generalized variable method. The generalized size, generalized adjusted and unadjusted powers of the test, generalized coverage probabilities are also discussed by comparing with their classical counterparts.
The Weibull distribution, frequently used for life data analysis, is composited with inverse Weib... more The Weibull distribution, frequently used for life data analysis, is composited with inverse Weibull distribution to obtain a computationally convenient parametric distribution for modeling reliability data. This two-parameter smooth and continuous natural composition has an inverse Weibull density up to an unknown threshold value and Weibull density for the remainder. The resulting density is similar in shape to the inverse Weibull density, yet its upper tail is lighter than the Weibull density. And, the right-tail behavior is quite similar to the Weibull density. The least squares parameter estimation technique is discussed by analyzing a repair time reliability data.
Physical measurements like dimensions, including time, and angles in scientific experiments are f... more Physical measurements like dimensions, including time, and angles in scientific experiments are frequently recorded without their algebraic sign. The directions of those physical quantities measured with respect to a frame of reference in most practical applications are considered to be unimportant and are ignored. As a consequence, the underlying distribution of measurements is replaced by a distribution of absolute measurements. When the underlying distribution is logistic, the resulting distribution is called the “folded logistic distribution”. Here, the properties of the folded logistic distribution will be presented and the techniques for estimating parameters will be given. The advantages of using this folded logistic distribution over the folded normal distribution will be discussed and some examples will be cited.
Journal of Statistical Computation and Simulation, 2014
This paper considers the development of inferential techniques based on the generalized variable ... more This paper considers the development of inferential techniques based on the generalized variable method (GV-Method) for the location parameter of the general half-normal distribution. We are interested in hypothesis testing of, and interval estimation for, the location parameter. Body fat data, urinary excretion rate data, and simulated data are used to illustrate the application and to demonstrate the advantages of the proposed GV-Method over the large-sample method and the Bayesian method.
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Papers by Sumith Gunasekera