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This paper deals with statistical inference for lifetime data in presence of imperfect maintenance. For the maintenance model, the Sheu and Griffith model is considered. The lifetime distribution belongs to exponential distribution class. The maximum likelihood estimation procedure of the model parameters is discussed, and confidence intervals are provided using the asymptotic likelihood theory and bootstrap approach. Based on conjugate and discrete priors, Bayesian estimators of the model parameters are developed under symmetric and asymmetric loss functions. The proposed methodologies are applied to simulated data and sensitivity analysis to different parameters and data characteristics is carried out. The effect of model misspecification is also assessed within this class of distributions through a Monte Carlo simulation study. Finally, two datasets are analyzed for demonstrative aims. [ABSTRACT FROM AUTHOR]

In this paper, the inference of multicomponent stress-strength reliability has been derived using progressively censored samples from Topp-Leone distribution. Both stress and strength variables are assumed to follow Topp-Leone distributions with different shape parameters. The maximum likelihood estimate along with the asymptotic confidence interval are developed. Boot-p and Boot-t confidence intervals are also constructed. The Bayes estimates under generalized entropy loss function based on gamma priors using Lindley's, Tierney-Kadane's approximation and Markov chain Monte Carlo methods are derived. A simulation study is considered to check the performance of various estimation methods and different censoring schemes. A real data study shows the applicability of the proposed estimation methods. [ABSTRACT FROM AUTHOR]

AbstractThe main objective of this paper is to propose a new general family of distributions, namely compound truncated Poisson log-normal distribution of which log-normal distribution is a special case. The proposed model has three unknown parameters, and it can take variety of shapes. It can be used effectively in analyzing maximum precipitation data during a particular period of time obtained from different stations. It is assumed that the number of stations operate follows a zero-truncated Poisson random variables, and the daily precipitation follows a log-normal random variable. The maximum likelihood estimators can be obtained quite conveniently using Expectation-Maximization (EM) algorithm. Approximate maximum likelihood estimators are also derived. The associated confidence intervals can also be obtained from the observed Fisher information matrix. Simulation results have been performed to check the performance of the EM algorithm, and it is observed that the EM algorithm works quite well in this case. When we analyze the precipitation data set using the proposed model it is observed that the proposed model provides better fit than some of the existing models. [ABSTRACT FROM AUTHOR]

Lomax distribution has been widely used in economics, business and actuarial sciences. Due to its importance, we consider the statistical inference of this model under joint type-II censoring scenario. In order to estimate the parameters, we derive the Newton-Raphson(NR) procedure and we observe that most of the times in the simulation NR algorithm does not converge. Consequently, we make use of the expectation-maximization (EM) algorithm. Moreover, Bayesian estimations are also provided based on squared error, linear-exponential and generalized entropy loss functions together with the importance sampling method due to the structure of posterior density function. In the sequel, we perform a Monte Carlo simulation experiment to compare the performances of the listed methods. Mean squared error values, averages of estimated values as well as coverage probabilities and average interval lengths are considered to compare the performances of different methods. The approximate confidence intervals, bootstrap-p and bootstrap-t confidence intervals are computed for EM estimations. Also, Bayesian coverage probabilities and credible intervals are obtained. Finally, we consider the Bladder Cancer data to illustrate the applicability of the methods covered in the paper. [ABSTRACT FROM AUTHOR]

This paper deals with a new two-parameter lifetime distribution with increasing, decreasing and constant hazard rate. This distribution allows the occurrence of zero values and involves the exponential, linear exponential and other combinations of Weibull distributions as submodels. Many statistical properties of the distribution are derived. Maximum likelihood estimation of the parameters and a bias corrective approach is investigated with a simulation study for performance of the estimators. Four real data sets are analyzed for illustrative purposes and it is noted that the distribution is a highly alternative to the gamma, Weibull, Lognormal and exponentiated exponential distributions. [ABSTRACT FROM AUTHOR]

In this paper, competing risks model is considered when causes of failure are dependent. When latent failure times are distributed by the Marshall-Olkin bivariate Kumaraswamy model, inference for the unknown model parameters is studied under a generalized progressive hybrid censoring. Maximum likelihood estimates of unknown parameters are established, and the associated existence and uniqueness are provided. The approximate confidence intervals are constructed via the observed Fisher information matrix. Moreover, Bayes estimates and the credible intervals of the unknown parameters are also presented based a flexible Gamma-Dirichlet prior, and the importance sampling method is used to compute associated estimates. Simulation study and a lifetime example are given for illustration purposes. [ABSTRACT FROM AUTHOR]

In the last decade, Diáz-Garciá and Leiva-Sánchez (2005, 2007) proposed a generalized Birnbaum-Saunders distribution based on elliptically contoured distributions. A special case of this generalization is Student's t Birnbaum-Saunders distribution. This flexible lifetime distribution generalizes both the Cauchy Birnbaum-Saunders distribution and the two-parameter Birnbaum-Saunders distribution. In this comparison paper, we discuss maximum likelihood estimation methods for the parameters of this distribution. We numerically illustrate and examine the performances of all discussed methods using extensive Monte Carlo simulations and illustrative examples. Furthermore, we analyze real-life data to assess the practical usage of the considered generalized family of distributions, and to illustrate the discussed estimation methods. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the maximum likelihood estimation for the reflected Ornstein-Uhlenbeck processes with jumps based on continuous observations. We derive likelihood functions by using semimartingale theory. From this we get explicit formulas for estimators. The strong consistence and asymptotic normality of estimators are proved by using the method of stochastic integration. [ABSTRACT FROM AUTHOR]

In this paper, based on hybrid censored sample from a two parameter exponentiated half logistic distribution, we consider the problem of estimating the unknown parameters using frequentist and Bayesian approaches. Expectation-Maximization, Lindley's approximation and Metropolis-Hastings algorithms are used for obtaining point estimators and corresponding confidence intervals for the shape and scale parameters involved in the underlying model. Data analyses involving the survival times of patients suffering from cancer diseases and treated radiotherapy and/or chemotherapy have been performed. Finally, numerical simulation study was conducted to assess the performances of the so developed methods and conclusions on our findings are reported. [ABSTRACT FROM AUTHOR]

Ranked set sampling (RSS) has been proved to be an efficient sampling design for parametric and non-parametric inference. In this paper, we consider RSS-based estimation for the two-parameter Birnbaum–Saunders (BS) distribution, which is widely used in reliability analysis. The estimation methods considered for comparison purposes were: maximum likelihood (ML), modified method of moments (MMM), maximum product of spacings (MPS), and Anderson–Darling (AD). The performance of the RSS-based estimators was evaluated through Monte Carlo simulations under both perfect and imperfect ranking assumptions. The bias, mean squared error, and mean integrated squared error were used as the criteria for comparison. The results revealed that the RSS-based estimators perform better than their simple random sampling (SRS) counterparts. The ML estimator performed the best under the perfect ranking assumption, while the MMM provided better performance for higher levels of imperfect ranking. Additional simulations based on data from a forest inventory corroborated our findings. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new method of estimation for the parameters and quantiles of the three-parameter Weibull distribution based on Type-II right censored data. The method, based on a data transformation, overcomes the problem of unbounded likelihood. In the proposed method, under mild conditions, the estimates always exist uniquely, and the estimators are also consistent over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method of estimation performs well compared to some prominent methods in terms of bias and root mean squared error in small-sample situations. Finally, two real data sets are used to illustrate the proposed method of estimation. [ABSTRACT FROM PUBLISHER]

In this paper, we propose a method of estimation of parameters and quantiles of the three-parameter gamma distribution based on Type-II right-censored data. In the proposed method, under mild conditions, the estimates always exist uniquely, and the estimators have consistency over the entire parameter space. Through Monte Carlo simulations, we further show that the proposed method performs well compared with another prominent method of estimation in terms of bias and root mean-squared error in small-sample situations. Finally, two real data sets are used for illustrating the proposed method. [ABSTRACT FROM PUBLISHER]

In this paper, the maximum likelihood (ML) and Bayes, by using Markov chain Monte Carlo (MCMC), methods are considered to estimate the parameters of three-parameter modified Weibull distribution (MWD(β, τ, λ)) based on a right censored sample of generalized order statistics (gos). Simulation experiments are conducted to demonstrate the efficiency of the proposed methods. Some comparisons are carried out between the ML and Bayes methods by computing the mean squared errors (MSEs), Akaike's information criteria (AIC) and Bayesian information criteria (BIC) of the estimates to illustrate the paper. Three real data sets from Weibull(α, β) distribution are introduced and analyzed using the MWD(β, τ, λ) and also using the Weibull(α, β) distribution. A comparison is carried out between the mentioned models based on the corresponding Kolmogorov–Smirnov (K–S) test statistic, {AIC and BIC} to emphasize that the MWD(β, τ, λ) fits the data better than the other distribution. All parameters are estimated based on type-II censored sample, censored upper record values and progressively type-II censored sample which are generated from the real data sets. [ABSTRACT FROM PUBLISHER]

Ranked set sampling (RSS) is an efficient method for estimating parameters when exact measurement of observation is difficult and/or expensive. In this paper, we provide maximum likelihood estimation of the shape and scale parameters concerning generalized Rayleigh distribution based on RSS and its some modifications. We compare the biases, mean squared errors and relative efficiencies of estimators in simple random sampling, RSS, extreme RSS and median RSS with different set and cycle sizes. Comparison of the mean squared errors of estimators in RSS for the case of imperfect ranking are also given. Monte Carlo simulation study is performed by using Mathematica 11.0 with 10,000 repetitions. [ABSTRACT FROM AUTHOR]

This paper develops Bayesian analysis in the context of progressively Type II censored data from the compound Rayleigh distribution. The maximum likelihood and Bayes estimates along with associated posterior risks are derived for reliability performances under balanced loss functions by assuming continuous priors for parameters of the distribution. A practical example is used to illustrate the estimation methods. A simulation study has been carried out to compare the performance of estimates. The study indicates that Bayesian estimation should be preferred over maximum likelihood estimation. In Bayesian estimation, the balance general entropy loss function can be effectively employed for optimal decision-making. [ABSTRACT FROM PUBLISHER]

In this paper, a new extension for the generalized Rayleigh distribution is introduced. The proposed model, called Marshall–Olkin extended generalized Rayleigh distribution, arises based on the scheme introduced by Marshall and Olkin (1997). A comprehensive account of the mathematical properties of the new distribution is provided. We discuss about the estimation of the model parameters based on two estimation methods. Empirical applications of the new model to real data are presented for illustrative purposes. [ABSTRACT FROM PUBLISHER]

A new method for generating new classes of distributions based on the probability-generating function is presented in Aly and Benkherouf [A new family of distributions based on probability generating functions. Sankhya B. 2011;73:70–80]. In particular, they focused their interest to the so-called Harris extended family of distributions. In this paper, we provide several general results regarding the Harris extended models such as the general behaviour of the failure rate function. We also derive a very useful representation for the Harris extended density function as an absolutely convergent power series of the survival function of the baseline distribution. Additionally, some stochastic order relations are established and limiting distributions of sample extremes are also considered for this model. These general results are illustrated in several special Harris extended models. Finally, we discuss estimation of the model parameters by the method of maximum likelihood and provide an application to real data for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, the problem of constant partially accelerated life tests when the lifetime follows the generalized exponential distribution is considered. Based on progressive type-II censoring scheme, the maximum likelihood and Bayes methods of estimation are used for estimating the distribution parameters and acceleration factor. A Monte Carlo simulation study is carried out to examine the performance of the obtained estimates. [ABSTRACT FROM AUTHOR]

In this paper, optimal accelerated life test (ALT) plans are investigated under progressive Type I interval censoring with random removals when lifetimes are Weibull distributed. The optimal ALT plans which minimize the asymptotic variance of the estimated qth quantile for different combinations of total number of inspections and removal probability are presented. For implementation convenience, the practical plans, which adopt the same optimality criterion but the inspection times are determined based on the ideas of equally spaced or equal probability scheme at each stress level, are also derived. Numerical studies are conducted to evaluate the relative efficiency of a practical plan to the corresponding optimal ALT plan. Some suggestions are given to experimenters for selecting an appropriate practical plan in designing an ALT under the proposed censoring scheme. [ABSTRACT FROM AUTHOR]

It is well known that general phase-type distributions are considerably overparameterized, that is, their representations often require many more parameters than is necessary to define the distributions. In addition, phase-type distributions, even those defined by a small number of parameters, may have representations of high order. These two problems have serious implications when using phase-type distributions to fit data. To address this issue we consider fitting data with the wider class of matrix-exponential distributions. Representations for matrix-exponential distributions do not need to have a simple probabilistic interpretation, and it is this relaxation which ensures that the problems of overparameterization and high order do not present themselves. However, when using matrix-exponential distributions to fit data, a problem arises because it is unknown, in general, when their representations actually correspond to a distribution. In this paper we develop a characterization for matrix-exponential distributions and use it in a method to fit data using maximum likelihood estimation. The fitting algorithm uses convex semi-infinite programming combined with a nonlinear search. [ABSTRACT FROM AUTHOR]

Here we consider an exponentiated version of the reduced Kies distribution and discuss some of its properties. The parameters of the distribution are estimated by the method of maximum likelihood and illustrated with the help of certain real-life data sets. Asymptotic behavior of the maximum likelihood estimators of the parameters of the distribution is also studied by using certain simulated data sets. [ABSTRACT FROM PUBLISHER]

In this article, we investigate the mathematical properties of the Lehmann type II inverse Weibull distribution. We show that this model is a reparameterized version of the Kumaraswamy-inverse Weibull distribution without identifiability problems. Parameter estimation is discussed using maximum likelihood (ML) method under a right-censoring scheme. Furthermore, a bootstrap resampling approach is considered to reduce the bias of the ML estimates. In order to illustrate the proposed methodology, we consider a real data set related to the failure time of devices in an aircraft. [ABSTRACT FROM AUTHOR]

We consider Type-I hybrid censored lifetimes from a two-parameter uniform distribution with support [a, b] and focus on the derivation of the exact distribution of the MLEs. In particular, we show that the distribution of the MLE is degenerated. Though the expressions for the distributions of the MLEs and do not necessarily involve B-splines, the key tool to derive these representations is a B-spline based integral identity established in Dahmen and Micchelli (1986). [ABSTRACT FROM AUTHOR]

We introduce a new family of distributions suitable for fitting positive data sets with high kurtosis which is called the Slashed Generalized Rayleigh Distribution. This distribution arises as the quotient of two independent random variables, one being a generalized Rayleigh distribution in the numerator and the other a power of the uniform distribution in the denominator. We present properties and carry out estimation of the model parameters by moment and maximum likelihood (ML) methods. Finally, we conduct a small simulation study to evaluate the performance of ML estimators and analyze real data sets to illustrate the usefulness of the new model. [ABSTRACT FROM AUTHOR]

Here, we introduce two-parameter compounded geometric distributions with monotone failure rates. These distributions are derived by compounding geometric distribution and zero-truncated Poisson distribution. Some statistical and reliability properties of the distributions are investigated. Parameters of the proposed distributions are estimated by the maximum likelihood method as well as through the minimum distance method of estimation. Performance of the estimates by both the methods of estimation is compared based on Monte Carlo simulations. An illustration with Air Crash casualties demonstrates that the distributions can be considered as a suitable model under several real situations. [ABSTRACT FROM PUBLISHER]

We investigate the small-sample quality of the maximum likelihood estimators (MLE) of the parameters of a zero-inflated Poisson distribution (ZIP). The finite-sample bias of the MLE is determined toO(n−1) using an analytic bias-reduction methodology based on the work of Cox and Snell (1968) and Cordeiro and Klein (1994). Monte Carlo simulations show that the MLEs have very small percentage biases for this distribution, but the analytic bias-reduction methods essentially eliminate the bias without adversely affecting the mean-squared errors of the estimators. The analytic adjustment compares favorably with the parametric bootstrap bias-corrected estimator, in terms of bias reduction itself, as well as with respect to mean-squared error and Pitman’s nearness measure. [ABSTRACT FROM AUTHOR]

We study a new family of distributions defined by the minimum of the Poisson random number of independent identically distributed random variables having a general exponentiated G distribution. Some mathematical properties of the new family including ordinary and incomplete moments, quantile and generating functions, mean deviations, order statistics and their moments, reliability, and Shannon entropy are derived. Maximum likelihood estimation of the model parameters is investigated. Two special models of the new family are discussed. We perform an application to a real data set to show the potentiality of the proposed family. [ABSTRACT FROM PUBLISHER]

The Maxwell (or Maxwell–Boltzmann) distribution was invented to solve the problems relating to physics and chemistry. It has also proved its strength of analysing the lifetime data. For this distribution, we consider point and interval estimation procedures in the presence of type-I progressively hybrid censored data. We obtain maximum likelihood estimator of the parameter and provide asymptotic and bootstrap confidence intervals of it. The Bayes estimates and Bayesian credible and highest posterior density intervals are obtained using inverted gamma prior. The expression of the expected number of failures in life testing experiment is also derived. The results are illustrated through the simulation study and analysis of a real data set is presented. [ABSTRACT FROM AUTHOR]

By running the life tests at higher stress levels than normal operating conditions, accelerated life testing quickly yields information on the lifetime distribution of a test unit. The lifetime at the design stress is then estimated through extrapolation using a regression model. In constant-stress testing, a unit is tested at a fixed stress level until failure or the termination time point of the test, while step-stress testing allows the experimenter to gradually increase the stress levels at some pre-fixed time points during the test. In this article, the optimalk-level constant-stress and step-stress accelerated life tests are compared for the exponential failure data under Type-I censoring. The objective is to quantify the advantage of using the step-stress testing relative to the constant-stress one. A log-linear relationship between the mean lifetime parameter and stress level is assumed and the cumulative exposure model holds for the effect of changing stress in step-stress testing. The optimal design point is then determined under C-optimality, D-optimality, and A-optimality criteria. The efficiency of step-stress testing compared to constant-stress testing is discussed in terms of the ratio of optimal objective functions based on the information matrix. [ABSTRACT FROM AUTHOR]

In applications of IRT, it often happens that many examinees omit a substantial proportion of item responses. This can occur for various reasons, though it may well be due to no more than the simple fact of design incompleteness. In such circumstances, literature not infrequently refers to various types of estimation problem, often in terms of generic “convergence problems” in the software used to estimate model parameters. With reference to the Partial Credit Model and the instance of data missing at random, this article demonstrates that as their number increases, so does that ofanomalousdatasets, intended as those not corresponding to a finite estimate of (the vector parameter that identifies) the model. Moreover, the necessary and sufficient conditions for the existence and uniqueness of the maximum likelihood estimation of the Partial Credit Model (and hence, in particular, the Rasch model) in the case of incomplete data are given – with reference to the model in its more general form, the number of response categories varying according to item. A taxonomy of possible cases of anomaly is then presented, together with an algorithm useful in diagnostics. [ABSTRACT FROM AUTHOR]

The maximum likelihood system of equations for the shape and scale parameters ξ and β of a generalized Pareto distribution is summarized through a single equation h x (ρ) = 0 where x designates the n -sample of realizations and . The study of the function h x (ρ) in the neighborhood of 0 puts forward a simple statistic S (x) only based on the first two empirical moments which is independent from β. This statistic allows to build an immediate and easy to use statistical test for ξ. The power of this test appears as quite similar to the one of already known test procedures which are much more difficult to use in practice. Moreover, the maximum likelihood solution of h x (ρ) = 0, say ρ, and S (x) both have the same sign. This property allows us to propose a controlled use of standard optimization algorithms for characterizing ρ, and as a consequence, the maximum likelihood estimations of ξ and β, without any risk of convergence failure or aberrant solution. [ABSTRACT FROM AUTHOR]