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In this paper, the stress–strength reliability $ R_{s,k} $ R s , k of a multicomponent s-out-of-k system for exponentiated Gumbel distribution is considered. An s-out-of-k system means a system with total k components and the system can survive only when atleast s of the total components function properly. The ability of the system to overcome the experiencing stress with its strength is termed as its stress–strengh reliability. The maximum likelihood estimator and Bayes estimator for $ R_{s,k} $ R s , k are obtained. The Bayes estimators are obtained using Markov chain Monte Carlo(MCMC) method under both symmetric and asymmetric loss functions. The loss functions we considered are squared error loss function, LINEX loss function and entropy loss function. The asymptotic, bootstrap and highest posterior density(HPD) confidence intervals for $ R_{s,k} $ R s , k are also obtained. A simulation study is conducted for evaluating the efficiency of the estimators derived in this paper. Real data sets are also considered for illustration. [ABSTRACT FROM AUTHOR]

In this paper, we focus on studying the Mixed-Effects State-Space (MESS) models previously introduced by Liu et al. [Liu D, Lu T, Niu X-F, et al. Mixed-effects state-space models for analysis of longitudinal dynamic systems. Biometrics. 2011;67(2):476–485]. We propose an estimation method by combining the auxiliary particle learning and smoothing approach with the Expectation Maximization (EM) algorithm. First, we describe the technical details of the algorithm steps. Then, we evaluate their effectiveness and goodness of fit through a simulation study. Our method requires expressing the posterior distribution for the random effects using a sufficient statistic that can be updated recursively, thus enabling its application to various model formulations including non-Gaussian and nonlinear cases. Finally, we demonstrate the usefulness of our method and its capability to handle the missing data problem through an application to a real dataset. [ABSTRACT FROM AUTHOR]

The two-parameter Rayleigh distribution, as an extended distribution of the Rayleigh distribution, has been widely applied in reliability analysis. With the introduction of the location parameter, two-parameter Rayleigh distribution becomes more flexible in fitting real-data. In this paper, based on generalized progressively hybrid censored(GPHC) sample from the two-parameter Rayleigh distribution, Classical and Bayesian inferences are discussed. The Newton-Raphson(NR) and Expectation-Maximization(EM) algorithms are used to compute the maximum likelihood estimates(MLEs). As well as the asymptotic confidence interval(ACI) estimation is obtained through the asymptotic distribution theory of maximum likelihood estimation(MLE) and computation of the observed Fisher information matrix. In Bayesian frame, the estimation of unknown parameters and prediction of future observable are taken into consideration. Due to Bayesian estimation is challenging to compute precisely and for the purpose of comparison, the Lindley's approximation, the Tierney-Kadane(TK) approximation and Markov chain Monte Carlo(MCMC) method are employed to obtain Bayesian estimates. Then, combining the MCMC algorithm mentioned in the article, the one- and two- samples Bayesian prediction are obtained. Finally, the simulation results are provided and a real-life data set is used for illustration purpose. [ABSTRACT FROM AUTHOR]

In this paper we describe a methodology for parameter estimation of multivariate distributions defined as normal mean-variance mixture where the mixing random variable is rapidly decreasing tempered stable distributed. We address some numerical issues resulting from the use of the characteristic function for density approximation. We focus our attention on the practical implementation of numerical methods involving the use of these multivariate distributions in the field of finance and we empirical assess the proposed algorithm through an analysis on a five-dimensional series of stock index log-returns. [ABSTRACT FROM AUTHOR]

A popular way to estimate the parameters of a hidden Markov model (HMM) is direct numerical maximization (DNM) of the (log-)likelihood function. The advantages of employing the TMB [Kristensen K, Nielsen A, Berg C, et al. TMB: automatic differentiation and Laplace approximation. J Stat Softw Articles. 2016;70(5):1–21] framework in R for this purpose were illustrated recently [Bacri T, Berentsen GD, Bulla J, et al. A gentle tutorial on accelerated parameter and confidence interval estimation for hidden Markov models using template model builder. Biom J. 2022 Oct;64(7):1260–1288]. In this paper, we present extensions of these results in two directions. First, we present a practical way to obtain uncertainty estimates in form of confidence intervals (CIs) for the so-called smoothing probabilities at moderate computational and programming effort via TMB. Our approach thus permits to avoid computer-intensive bootstrap methods. By means of several examples, we illustrate patterns present for the derived CIs. Secondly, we investigate the performance of popular optimizers available in R when estimating HMMs via DNM. Hereby, our focus lies on the potential benefits of employing TMB. Investigated criteria via a number of simulation studies are convergence speed, accuracy, and the impact of (poor) initial values. Our findings suggest that all optimizers considered benefit in terms of speed from using the gradient supplied by TMB. When supplying both gradient and Hessian from TMB, the number of iterations reduces, suggesting a more efficient convergence to the maximum of the log-likelihood. Last, we briefly point out potential advantages of a hybrid approach. [ABSTRACT FROM AUTHOR]

In this paper, we consider the estimation of a multicomponent stress–strength reliability when stress and strength variables follow unit Bur XII distribution. In estimation procedure, the maximum likelihood and Bayesian methods are used. The maximum likelihood estimator is obtained via iterative methods. The asymptotic confidence interval is constructed using asymptotic properties of the corresponding estimator. In addition, two bootstrap confidence intervals are constructed. Bayesian estimator is obtained using three different approximation methods: Lindley's approximation, Tierney–Kadane approximation and Markov Chain Monte Carlo method. The interval estimation based on Bayesian method is studied. The simulation study is conducted to investigate and compare the performance of the considered methods. Finally, an original data set, general dam occupancy rate of Istanbul, Turkey obtained from Istanbul Statistic Office, is analysed in the concept of multicomponent stress–strength reliability. [ABSTRACT FROM AUTHOR]

Recently, the varying-coefficient additive model (VCAM) has received much attention due to its flexibility and interpretability. In this paper, we consider its generalized form, called a generalized varyingcoefficient additive model (GVCAM), which can model discrete and continuous responses for locally stationary covariates. Specifically, the conditional mean function is specified via a link function g and a nonparametric part given by a VCAM. We develop a pilotestimation- based local linear maximum likelihood estimator (PEBLLE) to approximate the univariate component function. We also show the proposed estimators are oracle efficient and present the pointwise asymptotic distribution as well as simultaneous confidence bands. Simulation studies investigating the finite-sample performance of the proposed methodology are considered, and a real data application illustrating our method is also given. [ABSTRACT FROM AUTHOR]

Adaptive Type-II progressive hybrid censoring scheme has quite popular in a life-testing problem and reliability analysis due to it ensures more efficiency of inference procedures and saves total testing time. In this paper, an adaptive Type-II progressive hybrid censored sampling with random removals is considered, where the removals of the survival units at each stage from a life-test follows a binomial distribution during the execution of the experiment. The classical and Bayesian approaches are used to obtain the point and interval estimates of the unknown parameters of Weibull distribution, when the lifetimes are collected under the proposed censoring scheme. Different Bayesian estimates relative to various balanced type loss functions are obtained. Due to the complexity of the proposed estimators, some numerical techniques are implemented to obtain them. Using Markov chain Monte Carlo methods, the different Bayes estimates and associate credible intervals are developed. Extensive simulation study is performed to examine the efficiency of the proposed estimators. To show the applicability of the proposed methods in a real-life scenario, two real data sets coming from clinical and engineering areas are analysed. [ABSTRACT FROM AUTHOR]

This paper proposes a bias-corrected expression for maximum likelihood estimators using the sequential number-theoretic method for optimization (SNTO) to improve the efficiency and accuracy of the estimators in three extreme value distributions (EVDs). It is well known that the widely used maximum likelihood estimation (MLE) could be often biased for small-size samples in EVDs. Meanwhile, numerical simulation results reveal that maximum likelihood estimators are suffered from high variance when the sample size is small and the impact is non-negligible. A comprehensive comparison study which includes classical bias-corrected methods and more recent ones is presented. Based on the simulation studies, the bias-correction estimator via SNTO is highly recommended to reduce the bias and variance of estimators. In addition, a real data set is illustrated to employ different techniques. [ABSTRACT FROM AUTHOR]

The aim of the paper is to estimate the unknown parameters of weighted exponential distribution based on the competing risks model under progressively Type-II censoring. It is supposed that the latent causes of failures have weighted exponential distributions with different parameters. The maximum likelihood estimations of four unknown parameters are derived and the uniqueness and existence of them are theoretically proved. Moreover, approximate intervals are proposed and constructed with the delta method and Fisher information matrix. Bootstrap methods are also applied to calculate the confidence intervals. Furthermore, Bayes estimates and the corresponding credible intervals under three various loss functions are computed by using the Monte Carlo Markov Chain method. A simulation study is conducted to assess the statistical performance of all the estimators. Ultimately, real data analysis is provided to illustrate all the statistical inferential procedures developed in the paper. [ABSTRACT FROM AUTHOR]

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 generalized progressive hybrid censoring scheme (J-GPHCS) for two independent samples from different populations. We place both the samples simultaneously on the life testing experiment. Further, we assume the lifetime of the experimental units, under both samples, to follow exponential distribution with mean θ 1 and θ 2 , respectively. The maximum likelihood estimators, of the unknown parameters and their exact distributions, are derived. Asymptotic and bootstrap confidence intervals are also constructed. Further, the Bayesian inference of some unknown parametric functions is considered under a very flexible Inverse-Gamma priors. We also obtain the Bayes estimators, and associated credible intervals of the unknown parameters. Extensive simulation studies are performed to investigate the proposed estimators. Finally, the methods are illustrated with the analysis of a real data set. [ABSTRACT FROM AUTHOR]

In this paper, we discuss the problem of constant-stress accelerated life test when the failure data are progressive type-I interval censored. Both classical and Bayesian inferential approaches of the distribution parameters and reliability characteristics are discussed. In the classical scenario, the maximum likelihood estimates are approximated using the EM algorithm and the mid-point approximation method. Furthermore, the model's parameters are estimated by method of moments. Next in the Bayesian framework, the point estimates of unknown parameters are obtained using Tierney-Kadane's technique and Markov Chain Monte Carlo (MCMC) method. In addition, both approximate and credible confidence intervals (CIs) of the estimators are constructed. For illustration purpose, a Monte Carlo simulation is conducted to investigate the performance of the proposed estimators and a real data set is analysed. [ABSTRACT FROM AUTHOR]

The inverse generalized gamma (IGG) distribution can be particularly useful for modelling reliability (survival) data with an upside-down bathtub hazard rate function. The mathematical properties and estimation methods are not known in the literature. In this paper, we provide Bayesian inferences for the IGG distribution parameters using non-informative priors, namely, the Jeffreys prior and the reference prior. Extensive numerical simulations are conducted to investigate the performance of the proposed estimation method when compared with the classical inference. Finally, the potentiality of the IGG model is analysed by employing real environmental data. [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 consider Marshall-Olkin extended exponential (MOEE) distribution which is capable of modelling various shapes of failure rates and aging criteria. The purpose of this paper is three fold. First, we derive the maximum likelihood estimators of the unknown parameters and the observed the Fisher information matrix from progressively type-II censored data. Next, the Bayes estimates are evaluated by applying Lindley’s approximation method and Markov Chain Monte Carlo method under the squared error loss function. We have performed a simulation study in order to compare the proposed Bayes estimators with the maximum likelihood estimators. We also compute 95% asymptotic confidence interval and symmetric credible interval along with the coverage probability. Third, we consider one-sample and two-sample prediction problems based on the observed sample and provide appropriate predictive intervals under classical as well as Bayesian framework. Finally, we analyse a real data set to illustrate the results derived. [ABSTRACT FROM AUTHOR]

Modelling the covariance structure of multivariate longitudinal data is more challenging than its univariate counterpart, owing to the complex correlated structure among multiple responses. Furthermore, there are little methods focusing on the robustness of estimating the corresponding correlation matrix. In this paper, we propose an alternative Cholesky block decomposition (ACBD) for the covariance matrix of multivariate longitudinal data. The new unconstrained parameterization is capable to automatically eliminate the positive definiteness constraint of the covariance matrix and robustly estimate the correlation matrix with respect to the model misspecifications of the nested prediction error covariance matrices. The entries of the new decomposition are modelled by regression models, and the maximum likelihood estimators of the regression parameters in joint mean–covariance models are computed by a quasi-Fisher iterative algorithm. The resulting estimators are shown to be consistent and asymptotically normal. Simulations and real data analysis illustrate that the new method performs well. [ABSTRACT FROM AUTHOR]

Movements of equity indices are very important information for an investment decision. Empirical studies illustrate that the movements switch among different regimes. The Markov regime-switching model has important applications to such analysis. However, parameters estimated under normality assumption might not be stable and the corresponding change-point detection algorithm might face some challenges when either the error distribution is heavy-tailed or observed data contain outliers. In this paper, we relax the normality assumption and propose a generalized Markov regime-switching (GMRS) model. We propose a GMRS model based change-point detection algorithm, which is tested on both simulation data and Hang Seng monthly index. Simulation studies show that this algorithm can improve the accuracy of identifying change-points when either the error distribution is heavy-tailed or observed data contain outliers. It is also evident that the identified change-points on Hang Seng monthly index data match the observed market behaviours. [ABSTRACT FROM AUTHOR]

In the recent past, the autoregressive conditional duration (ACD) models have gained popularity in modelling the durations between successive events. The aim of this paper is to propose a simple and distribution free re-sampling procedure for developing the forecast intervals of linear ACD Models. We use the conditional least squares method to estimate the parameters of the ACD Model instead of the conditional Maximum Likelihood Estimation or Quasi-Maximum Likelihood Estimation and show that they are consistent for large samples. The properties of the proposed procedure are illustrated by a simulation study and an application to two real data sets. [ABSTRACT FROM AUTHOR]

In this paper, based on progressively Type-II censored samples, the problem of estimation of multicomponent stress–strength reliability under generalized half-normal (GHN) distribution is considered. The reliability of a k-component stress-strength system is estimated when both stress and strength variates are assumed to have a GHN distribution with various cases of same and different shape and scale parameters. Different methods such as the maximum likelihood estimates (MLEs) and Bayes estimation are discussed. The expectation maximization algorithm and approximate maximum likelihood methods are proposed to compute the MLE of reliability. The Lindley's approximation method, as well as Metropolis–Hastings algorithm, are applied to compute Bayes estimates. The performance of the proposed procedures is also demonstrated via a Monte Carlo simulation study and an illustrative example. [ABSTRACT FROM AUTHOR]

In this paper, we consider a constant stress accelerated life test terminated by a hybrid Type-I censoring at the first stress level. The model is based on a general log-location-scale lifetime distribution with mean life being a linear function of stress and with constant scale. We obtain the maximum likelihood estimators (MLE) and the approximate maximum likelihood estimators (AMLE) of the model parameters. Approximate confidence intervals, likelihood ratio tests and two bootstrap methods are used to construct confidence intervals for the unknown parameters of the Weibull and lognormal distributions using the MLEs. Finally, a simulation study and two illustrative examples are provided to demonstrate the performance of the developed inferential methods. [ABSTRACT FROM AUTHOR]

In earlier work, Kirchner [An estimation procedure for the Hawkes process. Quant Financ. 2017;17(4):571–595], we introduced a nonparametric estimation method for the Hawkes point process. In this paper, we present a simulation study that compares this specific nonparametric method to maximum-likelihood estimation. We find that the standard deviations of both estimation methods decrease as power-laws in the sample size. Moreover, the standard deviations are proportional. For example, for a specific Hawkes model, the standard deviation of the branching coefficient estimate is roughly 20% larger than for MLE – over all sample sizes considered. This factor becomes smaller when the true underlying branching coefficient becomes larger. In terms of runtime, our method clearly outperforms MLE. The present bias of our method can be well explained and controlled. As an incidental finding, we see that also MLE estimates seem to be significantly biased when the underlying Hawkes model is near criticality. This asks for a more rigorous analysis of the Hawkes likelihood and its optimization. [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 focuses on the development of a new extension of the generalized skew-normal distribution introduced in Gómez et al. [Generalized skew-normal models: properties and inference. Statistics. 2006;40(6):495–505]. To produce the generalization a new parameter is introduced, the signal of which has the flexibility of yielding unimodal as well as bimodal distributions. We study its properties, derive a stochastic representation and state some expressions that facilitate moments derivation. Maximum likelihood is implemented via the EM algorithm which is based on the stochastic representation derived. We show that the Fisher information matrix is singular and discuss ways of getting round this problem. An illustration using real data reveals that the model can capture well special data features such as bimodality and asymmetry. [ABSTRACT FROM PUBLISHER]

This paper deals with the problem of estimating unknown parameters of the Burr XII distribution under classical and Bayesian approaches when samples are observed under progressive type-I interval censoring. Under classical approach we employ the stochastic expectation maximization algorithm to obtain maximum likelihood estimators for the unknown parameters and also compute associated interval estimates. Further under Bayesian approach we obtain Bayes estimators with respect to different symmetric, asymmetric and balanced loss functions. In this regard we use Tierney–Kadane and Metropolis–Hastings (MH) algorithm. For illustration purpose we analyse a real data set and conduct a Monte Carlo simulation study to observe the performance of the proposed estimators. Finally we present a discussion on inspection times and optimal censoring. [ABSTRACT FROM PUBLISHER]

In this paper, we introduce a new family of transmuted distributions, the cubic rank transmutation map distribution. This new proposal increases the flexibility of the transmuted distributions enabling the modelling of more complex data such as ones possessing bimodal hazard rates. In order to illustrate the usefulness of the cubic rank transmutation map, we use two well-known lifetime distributions, namely the Weibull and log-logistic models. Several mathematical properties of these new distributions, namely the cubic rank transmuted Weibull distribution and the cubic rank transmuted log-logistic distribution, are derived. Then, the maximum likelihood estimation of the model parameters is described. A simulation study designed to assess the properties of this estimation procedure is then carried out. Finally, applications of the proposed models and their fit are illustrated with some datasets and the corresponding diagnostic analyses are also provided. [ABSTRACT FROM AUTHOR]

In this paper, a generalization of inverted exponential distribution is considered as a lifetime model [A.M. Abouammoh and A.M. Alshingiti,Reliability estimation of generalized inverted exponential distribution, J. Statist. Comput. Simul. 79(11) (2009), pp. 1301–1315]. Its reliability characteristics and important distributional properties are discussed. Maximum likelihood estimation of the two parameters involved along with reliability and failure rate functions are derived. The method of least square estimation of parameters is also studied here. In view of cost and time constraints, type II progressively right censored sampling scheme has been used. For illustration of the performance of the estimates, a Monte Carlo simulation study is carried out. Finally, a real data example is given to show the practical applications of the paper. [ABSTRACT FROM AUTHOR]

In this paper, based on an adaptive Type-II progressively censored sample from the generalized exponential distribution, the maximum likelihood and Bayesian estimators are derived for the unknown parameters as well as the reliability and hazard functions. Also, the approximate confidence intervals of the unknown parameters, and the reliability and hazard functions are calculated. Markov chain Monte Carlo method is applied to carry out a Bayesian estimation procedure and in turn calculate the credible intervals. Moreover, results from simulation studies assessing the performance of our proposed method are included. Finally, an illustrative example using real data set is presented for illustrating all the inferential procedures developed here. [ABSTRACT FROM AUTHOR]

In this paper, a generalized version of the intervened negative binomial distribution of Kumar and Sreeja [On intervened negative binomial distribution and some of its properties. Statistica. 2012;72:395–404] is considered and studied some of its properties. Certain methods of estimation of the parameters of the distribution are discussed and illustrated with the help of real life data sets. A test procedure is suggested for testing the intervention parameter and a simulation study is conducted for examining the performance of the estimators. [ABSTRACT FROM PUBLISHER]

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 many practical situations, complete data are not available in lifetime studies. Many of the available observations are right censored giving survival information up to a noted time and not the exact failure times. This constitutes randomly censored data. In this paper, we consider Maxwell distribution as a survival time model. The censoring time is also assumed to follow a Maxwell distribution with a different parameter. Maximum likelihood estimators and confidence intervals for the parameters are derived with randomly censored data. Bayes estimators are also developed with inverted gamma priors and generalized entropy loss function. A Monte Carlo simulation study is performed to compare the developed estimation procedures. A real data example is given at the end of the study. [ABSTRACT FROM AUTHOR]

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 we introduce a three-parameter lifetime distribution following the Marshall and Olkin [New method for adding a parameter to a family of distributions with application to the exponential and Weibull families. Biometrika. 1997;84(3):641–652] approach. The proposed distribution is a compound of the Lomax and Logarithmic distributions (LLD). We provide a comprehensive study of the mathematical properties of the LLD. In particular, the density function, the shape of the hazard rate function, a general expansion for moments, the density of therth order statistics, and the mean and median deviations of the LLD are derived and studied in detail. The maximum likelihood estimators of the three unknown parameters of LLD are obtained. The asymptotic confidence intervals for the parameters are also obtained based on asymptotic variance–covariance matrix. Finally, a real data set is analysed to show the potential of the new proposed distribution. [ABSTRACT FROM PUBLISHER]

An important drawback of the standard logarithmic series distribution (LSD) in several practical applications is that it excludes the zero observation from its support. The LSD with non-negative support is not much studied in the literature. Recently Kumar and Riyaz [On the zero-inflated LSD and its modification. Statistica (accepted for publication). 2013] considered a distribution in this respect namely ‘zero-inflated logarithmic series distribution (ZILSD)’. Through this paper we propose an alternative form of the ZILSD and study some of its properties. We obtain expressions for its probability-generating function, mean and variance, and develop certain recurrence relations for its probabilities, raw moments and factorial moments. The parameters of the model are estimated by the method of moments and the method of maximum likelihood, and certain test procedures are considered for testing the significance of the additional parameter of the distribution. The distribution has been fitted to certain real-life data sets for illustrating its usefulness compared with certain existing models available in the literature. Further, a simulation study is conducted for assessing the performance of the estimators. [ABSTRACT FROM PUBLISHER]

This paper investigates on the problem of parameter estimation in statistical model when observations are intervals assumed to be related to underlying crisp realizations of a random sample. The proposed approach relies on the extension of likelihood function in interval setting. A maximum likelihood estimate of the parameter of interest may then be defined as a crisp value maximizing the generalized likelihood function. Using the expectation-maximization (EM) to solve such maximizing problem therefore derives the so-called interval-valued EM algorithm (IEM), which makes it possible to solve a wide range of statistical problems involving interval-valued data. To show the performance of IEM, the following two classical problems are illustrated: univariate normal mean and variance estimation from interval-valued samples, and multiple linear/nonlinear regression with crisp inputs and interval output. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of estimating all the unknown parameters of geometric fractional Brownian processes from discrete observations. The estimation procedure is built upon the marriage of the quadratic variation and the maximum likelihood approach. The asymptotic properties of the estimators are provided. Moveover, we compare our derived method with the approach proposed by Misiran et al. [Fractional Black-Scholes models: complete MLE with application to fractional option pricing. In International conference on optimization and control; Guiyang, China; 2010. p. 573–586.], namely the complete maximum likelihood estimation. Simulation studies confirm theoretical findings and illustrate that our methodology is efficient and reliable. To show how to apply our approach in realistic contexts, an empirical study of Chinese financial market is also presented. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the Birnbaum–Saunders () power series class of distributions which is obtained by compoundingand power series distributions. The new class of distributions has as a particular case the two-parameterdistribution. The hazard rate function of the proposed class can be increasing and upside-down bathtub shaped. We provide important mathematical properties such as moments, order statistics, estimation of the parameters and inference for large sample. Three special cases of the new class are investigated with some details. We illustrate the usefulness of the new distributions by means of two applications to real data sets. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new three-parameter model called the exponential–Weibull distribution, which includes as special models some widely known lifetime distributions. Some mathematical properties of the proposed distribution are investigated. We derive four explicit expressions for the generalized ordinary moments and a general formula for the incomplete moments based on infinite sums of Meijer's G functions. We also obtain explicit expressions for the generating function and mean deviations. We estimate the model parameters by maximum likelihood and determine the observed information matrix. Some simulations are run to assess the performance of the maximum likelihood estimators. The flexibility of the new distribution is illustrated by means of an application to real data. [ABSTRACT FROM AUTHOR]

In this paper, we consider the distribution of life length of a series system with random number of components, sayZ. Considering the distribution ofZas generalized Poisson, an exponential-generalized Poisson (EGP) distribution is developed. The generalized Poisson distribution is a generalization of the Poisson distribution having one extra parameter. The structural properties of the resulting distribution are presented and the maximum likelihood estimation of the parameters is investigated. Extensive simulation studies are carried out to study the performance of the estimates. The score test is developed to test the importance of the extra parameter. For illustration, two real data sets are examined and it is shown that the EGP model, presented here, fits better than the exponential–Poisson distribution. [ABSTRACT FROM AUTHOR]

In this paper, based on a jointly type-II censored sample from two exponential populations, the Bayesian inference for the two unknown parameters are developed with the use of squared-error, linear-exponential and general entropy loss functions. The problem of predicting the future failure times, both point and interval prediction, based on the observed joint type-II censored data, is also addressed from a Bayesian viewpoint. A Monte Carlo simulation study is conducted to compare the Bayesian estimators with the maximum likelihood estimator developed by Balakrishnan and Rasouli [Exact likelihood inference for two exponential populations under joint type-II censoring. Comput Stat Data Anal. 2008;52:2725–2738]. Finally, a numerical example is utilized for the purpose of illustration. [ABSTRACT FROM AUTHOR]

In this paper, the statistical inference of the unknown parameters of a two-parameter inverse Weibull (IW) distribution based on the progressive type-II censored sample has been considered. The maximum likelihood estimators (MLEs) cannot be obtained in explicit forms, hence the approximate MLEs are proposed, which are in explicit forms. The Bayes and generalized Bayes estimators for the IW parameters and the reliability function based on the squared error and Linex loss functions are provided. The Bayes and generalized Bayes estimators cannot be obtained explicitly, hence Lindley's approximation is used to obtain the Bayes and generalized Bayes estimators. Furthermore, the highest posterior density credible intervals of the unknown parameters based on Gibbs sampling technique are computed, and using an optimality criterion the optimal censoring scheme has been suggested. Simulation experiments are performed to see the effectiveness of the different estimators. Finally, two data sets have been analysed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, the estimation of parameters for a three-parameter Weibull distribution based on progressively Type-II right censored sample is studied. Different estimation procedures for complete sample are generalized to the case with progressively censored data. These methods include the maximum likelihood estimators (MLEs), corrected MLEs, weighted MLEs, maximum product spacing estimators and least squares estimators. We also proposed the use of a censored estimation method with one-step bias-correction to obtain reliable initial estimates for iterative procedures. These methods are compared via a Monte Carlo simulation study in terms of their biases, root mean squared errors and their rates of obtaining reliable estimates. Recommendations are made from the simulation results and a numerical example is presented to illustrate all of the methods of inference developed here. [ABSTRACT FROM PUBLISHER]

This paper considers the design of accelerated life test (ALT) sampling plans under Type I progressive interval censoring with random removals. We assume that the lifetime of products follows a Weibull distribution. Two levels of constant stress higher than the use condition are used. The sample size and the acceptability constant that satisfy given levels of producer's risk and consumer's risk are found. In particular, the optimal stress level and the allocation proportion are obtained by minimizing the generalized asymptotic variance of the maximum likelihood estimators of the model parameters. Furthermore, for validation purposes, a Monte Carlo simulation is conducted to assess the true probability of acceptance for the derived sampling plans. [ABSTRACT FROM AUTHOR]

This article considers the maximum likelihood estimation (MLE) of a class of stationary and invertible vector autoregressive fractionally integrated moving-average (VARFIMA) processes considered in Equation (26) of Luceno [A fast likelihood approximation for vector general linear processes with long series: Application to fractional differencing, Biometrika 83 (1996), pp. 603-614] or Model A of Lobato [Consistency of the averaged cross-periodogram in long memory series, J. Time Ser. Anal. 18 (1997), pp. 137-155] where each component yi, t is a fractionally integrated process of order di, i=1, ..., r. Under the conditions outlined in Assumption 1 of this article, the conditional likelihood function of this class of VARFIMA models can be efficiently and exactly calculated with a conditional likelihood Durbin-Levinson (CLDL) algorithm proposed herein. This CLDL algorithm is based on the multivariate Durbin-Levinson algorithm of Whittle [On the fitting of multivariate autoregressions and the approximate canonical factorization of a spectral density matrix, Biometrika 50 (1963), pp. 129-134] and the conditional likelihood principle of Box and Jenkins [Time Series Analysis, Forecasting, and Control, 2nd ed., Holden-Day, San Francisco, CA]. Furthermore, the conditions in the aforementioned Assumption 1 are general enough to include the model considered in Andersen et al. [Modeling and forecasting realized volatility, Econometrica 71 (2003), 579-625] for describing the behaviour of realized volatility and the model studied in Haslett and Raftery [Space-time modelling with long-memory dependence: Assessing Ireland's wind power resource, Appl. Statist. 38 (1989), pp. 1-50] for spatial data as its special cases. As the computational cost of implementing the CLDL algorithm is much lower than that of using the algorithms proposed in Sowell [Maximum likelihood estimation of fractionally integrated time series models, Working paper, Carnegie-Mellon University], we are thus able to conduct a Monte Carlo experiment to investigate the finite sample performance of the CLDL algorithm for the 3-dimensional VARFIMA processes with the sample size of 400. The simulation results are very satisfactory and reveal the great potentials of using the CLDL method for empirical applications. [ABSTRACT FROM AUTHOR]

A generalized version of inverted exponential distribution (IED) is introduced in this paper. This lifetime distribution is capable of modelling various shapes of failure rates, and hence various shapes of ageing criteria. The model can be considered as another useful two-parameter generalization of the IED. Statistical and reliability properties of the generalized inverted exponential distribution are derived. Maximum likelihood estimation and least square estimation are used to evaluate the parameters and the reliability of the distribution. Properties of the estimates are also studied. [ABSTRACT FROM AUTHOR]

In this paper, the estimation of parameters based on a progressively type-I interval censored sample from a two-parameter Weibull distribution is studied. Different methods of estimation are discussed. They include the maximum likelihood estimation, method of moments, estimation based on Weibull probability plot, mid-point approximation method and one-step approximation method. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their biases and mean square errors. Some recommendations are made from the simulation results and a numerical example is presented to illustrate all of the methods of estimation developed here. [ABSTRACT FROM AUTHOR]

In this paper, step partially accelerated life tests are considered when the lifetime of an item under use condition follows a finite mixture of distributions. The analysis is performed when each of the components follows a general class of distributions, which includes, among others, the Weibull, compound Weibull (or three-parameter Burr type XII), power function, Gompertz and compound Gompertz distributions. Based on type-I censoring, the maximum likelihood estimates (MLEs) of the mixing proportions, scale parameters and acceleration factor are obtained. Special attention is paid to a mixture of two exponential components. Simulation results are obtained to study the precision of MLEs. [ABSTRACT FROM AUTHOR]

In this paper, the failure time of a device is observed under a higher stress subjected to a general class of stress-response model, when its distribution is a mixture of k components each of which represents a different cause of failure. The problem is studied when each of the components belongs to a general class of distributions which includes, among others, the Weibull, compound Weibull (or three-parameter Burr type XII), power function, Gompertz and compound Gompertz distributions. On the basis of the censored data, the maximum likelihood estimates of the unknown parameters involved under the general stress-response model are obtained. A special attention is paid to the power rule model applied to mixtures of two Weibull components. Mixtures of two exponentials, Rayleigh and Weibull components models are used as illustrative examples. [ABSTRACT FROM AUTHOR]