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Papers by majid hashempour

Research paper thumbnail of Bayes factors with sequential r-out-of-n system lifetimes

Research paper thumbnail of Characterizations on the basis of cumulative residual entropy of sequential order statistics

This article deals with the problem of characterizing the parent distribution on the basis of the... more This article deals with the problem of characterizing the parent distribution on the basis of the cumulative residual entropy of sequential order statistics under a conditional proportional hazard rates model. It is shown that the equality of the cumulative residual entropy in the first sequential order statistics determines uniquely the parent distribution. Subsequently, we characterize the Weibull distribution on the basis of the ratio of the cumulative residual entropy of first sequential order statistics to the corresponding mean. Also, we consider characterizations based on the dynamic cumulative residual entropy and derive some bounds for the cumulative residual entropy of residual lifetime of the sequential order statistics.

Research paper thumbnail of Testing Statistical Hypothesis of exponential populations with multiply sequential order statistics

Sequential order statistics (SOS) coming from non-homogeneous exponential distributions are consi... more Sequential order statistics (SOS) coming from non-homogeneous exponential distributions are considered in this paper. The generalized likelihood ratio (GLRT) and the Bayesian tests are derived for testing homogeneity of the exponential populations. It is shown that the GLRT in this case is also scale invariant. The maximum likelihood and the Bayesian estimates of parameters are derived on the basis of observed SOS samples. Explicit expression for SOS-based Bayes factor (BF) are derived.

Research paper thumbnail of Statistical evidences in sequential order statistics arising from a general family of lifetime distributions

In this paper, statistical evidences in sequential order statistics (SOS) coming from a general c... more In this paper, statistical evidences in sequential order statistics (SOS) coming from a general class of lifetime distributions, proposed by AL-Hussaini [1], is consid- ered. Weak and misleading evidences in multiply SOS samples for both simple and composite hypotheses about the parameters of interest are derived in explicit ex- pressions and their behaviours with respect to the model parameters are studied in details. In presence of nuisance parameters, the approximate evidences are also derived. Moreover, the types I and II Pareto family are investigated for illustrative purposes. Optimal sample sizes given a minimum desired level for the decisive and the correct probabilities are provided.

Research paper thumbnail of Mixture Representations of the Extropy of Conditional Mixed Systems and Their Information Properties

In this paper, we obtain the mixture representations for the extropy of a mixed used system and t... more In this paper, we obtain the mixture representations for the extropy of a mixed used system and the extropy of the inactivity time of a system. These representations demonstrate the extropy of conditional mixed systems as a mixture of a conditional coefficients vector, left (or right) truncated beta distribution, and the baseline distribution of the system components. Based on these representations, the comparisons of the extropy of conditional mixed systems are carried out with respect to the stochastic orders and stochastically ordered conditional coefficients vector between systems. Moreover, some bounds for the extropy of theses systems are derived. The utility of these representations is illustrated in two examples in which the extropy of a mixed used system and the extropy of the inactivity time of a system are computed and compared.

Research paper thumbnail of Estimation with Non-Homogeneous Sequential K-out-of-N System Lifetimes

Research paper thumbnail of A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations

In this paper, we introduce a new two-parameter lifetime distribution which is called extended Ha... more In this paper, we introduce a new two-parameter lifetime distribution which is called extended Half-Logistic (EHL) distribution. Theoretical properties of this model including the hazard function, quantile function, asymptotic, extreme value, moments, conditional moments, mean residual life, mean past lifetime, residual entropy, cumulative residual entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustration the purposes.

Research paper thumbnail of On invariant test with sequential order statistics: An open problem and some suggestions

Research paper thumbnail of Mathematics of evidences in dynamic systems with exponential component lifetimes and optimal sample size determination

In this paper, statistical evidences in lifetimes of sequential r-out-of-n systems, which are mod... more In this paper, statistical evidences in lifetimes of sequential r-out-of-n systems, which are modelled by the concept of sequential order statistics (SOS), coming from homogeneous exponential populations are considered. Weak and misleading evidences in SOS for hypotheses about the population parameter are derived in explicit expressions and their behaviours with respect to the model parameters are studied in details. Optimal sample sizes given a minimum desired level for the decisive and the correct probabilities are provided. It is shown that the optimal sample size does not depend on some model parameters.

Research paper thumbnail of Statistical Inference on the Basis of Sequential Order Statistics under a Linear Trend for Conditional Proportional Hazard Rates

Statistics, Optimization & Information Computing

This paper deals with systems consisting of independent and heterogeneous exponential components.... more This paper deals with systems consisting of independent and heterogeneous exponential components. Since failures of components may change lifetimes of surviving components because of load sharing, a linear trend for conditionally proportional hazard rates is considered. Estimates of parameters, both point and interval estimates, are derived on the basis of observed component failures for s(≥ 2) systems. Fisher information matrix of the available data is also obtained which can be used for studying asymptotic behaviour of estimates. The generalized likelihood ratio test is implemented for testing homogeneity of s systems. Illustrative examples are also given.

Research paper thumbnail of Evidences in lifetimes of sequential r-out-of-n systems and optimal sample size determination for Burr XII populations

Statistics, Optimization & Information Computing

In this paper, the statistical evidences in lifetimes of dynamic rout of -n systems, which are mo... more In this paper, the statistical evidences in lifetimes of dynamic rout of -n systems, which are modelled by sequential order statistics (SOS), are studied. Weak and misleading evidences in SOS for hypotheses concerning the population parameters are derived in explicit expressions and their behaviours with respect to the model parameters are investigated in details. Optimal sample sizes are provided while a minimum desired level for the decisive and the correct probabilities is given. It is shown that the optimal sample size does not depend on some model parameters.

Research paper thumbnail of Bayesian inference on multiply sequential order statistics from heterogeneous exponential populations with GLR test for homogeneity

Communications in Statistics - Theory and Methods, 2016

Research paper thumbnail of Dynamic Systems with Baseline Exponential Distribution Based on Sequential Order Statistics Under a Power Trend for Hazard Rates

Journal of Statistical Theory and Applications

This paper deals with analyzing dynamic engineering systems consisting of independent components.... more This paper deals with analyzing dynamic engineering systems consisting of independent components. The failure of a components causes more load on the surviving components. This property is modeled by a power trend conditionally proportional hazard rates. For modeling system lifetimes, the theory of sequential order statistics can be used. Sequential order statistics coming from heterogeneous exponential distributions are considered. The maximum likelihood and Bayesian estimates of the parameters are obtained in different cases. The generalized likelihood ratio and the Bayesian tests are also derived for testing homogeneity of the baseline exponential component lifetimes arising from s independent engineering systems.

Research paper thumbnail of Bayes factors with sequential r-out-of-n system lifetimes

Research paper thumbnail of Characterizations on the basis of cumulative residual entropy of sequential order statistics

This article deals with the problem of characterizing the parent distribution on the basis of the... more This article deals with the problem of characterizing the parent distribution on the basis of the cumulative residual entropy of sequential order statistics under a conditional proportional hazard rates model. It is shown that the equality of the cumulative residual entropy in the first sequential order statistics determines uniquely the parent distribution. Subsequently, we characterize the Weibull distribution on the basis of the ratio of the cumulative residual entropy of first sequential order statistics to the corresponding mean. Also, we consider characterizations based on the dynamic cumulative residual entropy and derive some bounds for the cumulative residual entropy of residual lifetime of the sequential order statistics.

Research paper thumbnail of Testing Statistical Hypothesis of exponential populations with multiply sequential order statistics

Sequential order statistics (SOS) coming from non-homogeneous exponential distributions are consi... more Sequential order statistics (SOS) coming from non-homogeneous exponential distributions are considered in this paper. The generalized likelihood ratio (GLRT) and the Bayesian tests are derived for testing homogeneity of the exponential populations. It is shown that the GLRT in this case is also scale invariant. The maximum likelihood and the Bayesian estimates of parameters are derived on the basis of observed SOS samples. Explicit expression for SOS-based Bayes factor (BF) are derived.

Research paper thumbnail of Statistical evidences in sequential order statistics arising from a general family of lifetime distributions

In this paper, statistical evidences in sequential order statistics (SOS) coming from a general c... more In this paper, statistical evidences in sequential order statistics (SOS) coming from a general class of lifetime distributions, proposed by AL-Hussaini [1], is consid- ered. Weak and misleading evidences in multiply SOS samples for both simple and composite hypotheses about the parameters of interest are derived in explicit ex- pressions and their behaviours with respect to the model parameters are studied in details. In presence of nuisance parameters, the approximate evidences are also derived. Moreover, the types I and II Pareto family are investigated for illustrative purposes. Optimal sample sizes given a minimum desired level for the decisive and the correct probabilities are provided.

Research paper thumbnail of Mixture Representations of the Extropy of Conditional Mixed Systems and Their Information Properties

In this paper, we obtain the mixture representations for the extropy of a mixed used system and t... more In this paper, we obtain the mixture representations for the extropy of a mixed used system and the extropy of the inactivity time of a system. These representations demonstrate the extropy of conditional mixed systems as a mixture of a conditional coefficients vector, left (or right) truncated beta distribution, and the baseline distribution of the system components. Based on these representations, the comparisons of the extropy of conditional mixed systems are carried out with respect to the stochastic orders and stochastically ordered conditional coefficients vector between systems. Moreover, some bounds for the extropy of theses systems are derived. The utility of these representations is illustrated in two examples in which the extropy of a mixed used system and the extropy of the inactivity time of a system are computed and compared.

Research paper thumbnail of Estimation with Non-Homogeneous Sequential K-out-of-N System Lifetimes

Research paper thumbnail of A new two-parameter lifetime distribution with flexible hazard rate function: Properties, applications and different method of estimations

In this paper, we introduce a new two-parameter lifetime distribution which is called extended Ha... more In this paper, we introduce a new two-parameter lifetime distribution which is called extended Half-Logistic (EHL) distribution. Theoretical properties of this model including the hazard function, quantile function, asymptotic, extreme value, moments, conditional moments, mean residual life, mean past lifetime, residual entropy, cumulative residual entropy and order statistics are derived and studied in details. The maximum likelihood estimates of parameters are compared with various methods of estimations by conducting a simulation study. Finally, two real data sets are illustration the purposes.

Research paper thumbnail of On invariant test with sequential order statistics: An open problem and some suggestions

Research paper thumbnail of Mathematics of evidences in dynamic systems with exponential component lifetimes and optimal sample size determination

In this paper, statistical evidences in lifetimes of sequential r-out-of-n systems, which are mod... more In this paper, statistical evidences in lifetimes of sequential r-out-of-n systems, which are modelled by the concept of sequential order statistics (SOS), coming from homogeneous exponential populations are considered. Weak and misleading evidences in SOS for hypotheses about the population parameter are derived in explicit expressions and their behaviours with respect to the model parameters are studied in details. Optimal sample sizes given a minimum desired level for the decisive and the correct probabilities are provided. It is shown that the optimal sample size does not depend on some model parameters.

Research paper thumbnail of Statistical Inference on the Basis of Sequential Order Statistics under a Linear Trend for Conditional Proportional Hazard Rates

Statistics, Optimization & Information Computing

This paper deals with systems consisting of independent and heterogeneous exponential components.... more This paper deals with systems consisting of independent and heterogeneous exponential components. Since failures of components may change lifetimes of surviving components because of load sharing, a linear trend for conditionally proportional hazard rates is considered. Estimates of parameters, both point and interval estimates, are derived on the basis of observed component failures for s(≥ 2) systems. Fisher information matrix of the available data is also obtained which can be used for studying asymptotic behaviour of estimates. The generalized likelihood ratio test is implemented for testing homogeneity of s systems. Illustrative examples are also given.

Research paper thumbnail of Evidences in lifetimes of sequential r-out-of-n systems and optimal sample size determination for Burr XII populations

Statistics, Optimization & Information Computing

In this paper, the statistical evidences in lifetimes of dynamic rout of -n systems, which are mo... more In this paper, the statistical evidences in lifetimes of dynamic rout of -n systems, which are modelled by sequential order statistics (SOS), are studied. Weak and misleading evidences in SOS for hypotheses concerning the population parameters are derived in explicit expressions and their behaviours with respect to the model parameters are investigated in details. Optimal sample sizes are provided while a minimum desired level for the decisive and the correct probabilities is given. It is shown that the optimal sample size does not depend on some model parameters.

Research paper thumbnail of Bayesian inference on multiply sequential order statistics from heterogeneous exponential populations with GLR test for homogeneity

Communications in Statistics - Theory and Methods, 2016

Research paper thumbnail of Dynamic Systems with Baseline Exponential Distribution Based on Sequential Order Statistics Under a Power Trend for Hazard Rates

Journal of Statistical Theory and Applications

This paper deals with analyzing dynamic engineering systems consisting of independent components.... more This paper deals with analyzing dynamic engineering systems consisting of independent components. The failure of a components causes more load on the surviving components. This property is modeled by a power trend conditionally proportional hazard rates. For modeling system lifetimes, the theory of sequential order statistics can be used. Sequential order statistics coming from heterogeneous exponential distributions are considered. The maximum likelihood and Bayesian estimates of the parameters are obtained in different cases. The generalized likelihood ratio and the Bayesian tests are also derived for testing homogeneity of the baseline exponential component lifetimes arising from s independent engineering systems.