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In this paper, a generalized autoregressive conditional heteroskedasticity model under skew-normal distributions is studied. A maximum likelihood approach is taken and the parameters in the model are estimated based on the expectation-maximization algorithm. The statistical diagnostics is made through the local influence technique, with the normal curvature and diagnostics results established for the model under four perturbation schemes in identifying possible influential observations. A simulation study is conducted to evaluate the performance of our proposed method and a real-world application is presented as an illustrative example. [ABSTRACT FROM AUTHOR]

AbstractIn this article, the parameter estimation of several commonly used two-parameter lifetime distributions, including the Weibull, inverse Gaussian, and Birnbaum–Saunders distributions, based on joint progressively Type-II right-censored sample is studied. Different numerical methods and algorithms are used to compute the maximum likelihood estimates of the unknown model parameters. These methods include the Newton–Raphson method, the stochastic expectation–maximization (SEM) algorithm, and the dual annealing (DA) algorithm. These estimation methods are compared in terms of accuracy (e.g. the bias and mean squared error), computational time and effort (e.g. the required number of iterations), the ability to obtain the largest value of the likelihood, and convergence issues by means of a Monte Carlo simulation study. Recommendations are made based on the simulated results. A real data set is analyzed for illustrative purposes. These methods are implemented in Python, and the computer programs are available from the authors upon request. [ABSTRACT FROM AUTHOR]

AbstractThis paper deals with the repair alert models. They are used for analyzing lifetime data coming from engineering devices under maintenance management. Repair alert models have been proposed and investigated for continuous component lifetimes. Existing studies are concerned with the lifetimes of items described by continuous distributions. However, discrete lifetimes are also frequently encountered in practice. Examples include operating a piece of equipment in cycles, reporting field failures that are gathered weekly, and the number of pages printed by a device completed before failure. Here, the repair alert models are developed when device lifetimes are discrete. A wide class of discrete distributions, called the telescopic family, is considered for the component lifetimes, and the proposed repair alert model is explained in detail. Furthermore, the problem of estimating parameters is investigated and illustrated by analyzing a real data set. [ABSTRACT FROM AUTHOR]

Nowadays, the confidentiality of data and information is of great importance for many companies and organizations. For this reason, they may prefer not to release exact data, but instead to grant researchers access to approximate data. For example, rather than providing the exact measurements of their clients, they may only provide researchers with grouped data, that is, the number of clients falling in each of a set of non-overlapping measurement intervals. The challenge is to estimate the mean and variance structure of the hidden ungrouped data based on the observed grouped data. To tackle this problem, this work considers the exact observed data likelihood and applies the Expectation-Maximization (EM) and Monte Carlo EM (MCEM) algorithms for cases where the hidden data follow a univariate, bivariate, or multivariate normal distribution. Simulation studies are conducted to evaluate the performance of the proposed EM and MCEM algorithms. The well-known Galton data set is considered as an application example. [ABSTRACT FROM AUTHOR]

The linear exponential distribution is a generalization of the exponential and Rayleigh distributions. This distribution is one of the best models to fit data with increasing failure rate (IFR). But it does not provide a reasonable fit for modeling data with decreasing failure rate (DFR) and bathtub shaped failure rate (BTFR). To overcome this drawback, we propose a new record-based transmuted generalized linear exponential (RTGLE) distribution by using the technique of Balakrishnan and He. The family of RTGLE distributions is more flexible to fit the data sets with IFR, DFR, and BTFR, and also generalizes several well-known models as well as some new record-based transmuted models. This paper aims to study the statistical properties of RTGLE distribution, like, the shape of the probability density function and hazard function, quantile function and its applications, moments and its generating function, order and record statistics, Rényi entropy. The maximum likelihood estimators, least squares and weighted least squares estimators, Anderson-Darling estimators, Cramér-von Mises estimators of the unknown parameters are constructed and their biases and mean squared errors are reported via Monte Carlo simulation study. Finally, the real data sets illustrate the goodness of fit and applicability of the proposed distribution; hence, suitable recommendations are forwarded. [ABSTRACT FROM AUTHOR]

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]

Dealing with competing risks is an important problem in reliability analysis and attracts much attention from scholars. It is more practical to consider competing risks with dependent failure causes in reality. In this article, statistical inference of the Marshall–Olkin bivariate Burr-XII distribution under adaptive type-II progressive hybrid censoring is discussed to show the procedure of dependent competing risks analysis in the complex data structure. The maximum likelihood estimation and lognormal approximation confidence intervals of parameters are computed. The existence and uniqueness of solutions are proved with Cauchy-Schwarz inequality. The Bayesian method with Gamma-Dirichlet prior and Metropolis-Hastings algorithm are further considered to find satisfied estimation of parameters. In addition, dynamic cumulative residual entropy is derived to quantify the information uncertainty of data. We finally compare the performance of various methods by conducting a simulation study and real data analysis. [ABSTRACT FROM AUTHOR]

In this paper, we focus on Bayesian estimation of the parameters in the geometric process (GP) in which the first occurrence time of an event is assumed to have Weibull distribution. The Bayesian estimators are derived based on both symmetric (Squared Error) and asymmetric (General Entropy, LINEX) loss functions. Since the Bayesian estimators of unknown parameters cannot be obtained analytically, Lindley's approximation and the Markov Chain Monte Carlo (MCMC) methods are applied to compute the Bayesian estimates. Furthermore, by using the MCMC methods, credible intervals of the parameters are constructed. Maximum likelihood (ML) estimators are also derived for unknown parameters. The confidence intervals of the parameters are obtained based on an asymptotic distribution of ML estimators. Moreover, the performances of the proposed Bayesian estimators are compared with the corresponding ML, modified moment and modified maximum likelihood estimators through an extensive simulation study. Finally, analyses of two different real data sets are presented for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we consider a transformation in a random variable which follows a bimodal Birnbaum-Saunders distribution. We propose the unit-bimodal Birnbaum-Saunders (UBBS) distribution and investigate some of its important properties, like cumulative distribution function, moments, survival function and risk function. We apply the UBBS distribution to censored data inflated at zero and one. We used the maximum likelihood approach for parameter estimation and to compare the models. Given the flexibility in UBBS distribution modes, our proposal performs best in beta regression models with zero and/or one excess. [ABSTRACT FROM AUTHOR]

Ranked set sampling with unequal set sizes (RSSU) are some of the important variants of ranked set sampling with equal set sizes (RSS). The sets that arise naturally in many applications are typically of different set sizes. One may prefer to use the largest sets available naturally along with the smaller sets rather than an attempt to form artificial equal-sized sets. This article develops maximum likelihood estimators for the location-scale family of distributions based on ranked set sampling with unequal set sizes (RSSU). The closed form expressions for MLE under RSSU do not exist, we have proved the existence of MLE for location and scale parameters for some standard distributions for RSSU data. It is proved that MLE based on MedRSSU are more efficient than their counterparts based on SRS for some standard distributions for location-scale parameters. It is also shown that asymptotic efficiencies of the MLE based on MedRSSU are considerably better than those of the estimators based on RSS with the same number of observations. A simulation study is conducted to compare the performances of the MLE's from RSS and MedRSSU with the corresponding SRS estimators when the underlying distributions are normal and logistic. [ABSTRACT FROM AUTHOR]

A copula-based Markov chain model can flexibly capture serial dependence in a time series. However, the computational developments for copula-based Markov models remain insufficient for discrete marginal models compared with continuous ones. In this article, we develop computational methods for a binomial time series under the Clayton and Joe copulas. The methods include the data-generation, parameter estimation, model selection, and goodness-of-fit tests. We implement the methods in our R package Copula.Markov (). We conduct simulations to see the performance of the developed methods. Finally, the proposed method is illustrated by a real dataset. [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]

Cure models are widely popular in modeling time-to-event data that are characterized by cure fraction owing to long-term survivors. Mixture cure models are perhaps the most studied cure models in the literature. In this article, however, we consider a competing risks scenario where the number of competing causes is modeled by flexible Conway-Maxwell (COM) Poisson distribution, and the lifetimes corresponding to the competing causes are assumed to be independently distributed following proportional hazards model. The baseline hazard function is modeled by a piecewise linear function, and hence, estimated non parametrically. Probability of obtaining zero competing causes is used to estimate the cure rate. Collectively, the resultant cure model is exceedingly general and flexible. The estimation of the parameters is carried out using maximum likelihood (ML) method by implementing the expectation-maximization (EM) algorithm, except for the dispersion parameter of the COM-Poisson distribution, which is estimated by the profile likelihood method. The performance of the model is tested under various settings of censoring rate, sample size and mean lifetime. Discrimination of models is performed and carried out with likelihood-based and information-based criteria. Performance of the proposed model is further illustrated using a real-world data on cutaneous melanoma. [ABSTRACT FROM AUTHOR]

Mixtures of two-component normal distributions (MixN) have various applications in statistical inference with flexibility in density fitting. The best estimation of the five model parameters still represents a challenge. This article proposes more accurate density fittings given a random sample in both the moment-based and likelihood-based estimation frameworks. Motivated by the excellent performance of the Quasi-Monte Carlo method in quantile estimations, we propose an innovative approach to improve the accuracy of parameter estimations by reinforcing the representativeness of observed data via the distribution-free Harrell-Davis quantile estimators. The revision on the penalized maximum likelihood method is also considered due to the unpleasant properties of the original likelihood function under MixN. The bootstrap bias-corrected moment estimators are given as another revision. A sequential algorithm for optimization (SNTO) is conducted in finding numerical solutions for the two types of parameter estimation methods. SNTO is more adapted to MixN and shows strong advantages in the likelihood-based estimation compared to the famous EM algorithm. Simulation results show that our proposed approach can effectively improve estimation accuracy and increase resistance to small sample sizes and/or high percent overlaps between two mixture components. A real data example is given to illustrate the efficiency of our proposed methods. [ABSTRACT FROM AUTHOR]

Gompertz distribution is a significant and practical continuous lifetime distribution, which plays an important role in reliability engineering. A Gompertz distribution competing risks model is discussed and studied under general progressive censoring in this paper. When the lifetime model fails for different latent reasons, the maximum likelihood estimates are given for the unknown parameters. The approximate confidence intervals through Fisher information matrix and bootstrap confidence intervals are established, containing bootstrap-p and bootstrap-t techniques. In addition, the Bayes estimation of unknown parameters is investigated under the condition of squared error loss. Moreover, the Bayes credible interval is derived. Finally, a numerical simulation is conducted to evaluate the performances of the proposed methods and real-life data is analyzed by applying the proposed inference methods. [ABSTRACT FROM AUTHOR]

Recently, the progressive Type-II censoring has been extended to a more general censoring scheme, called joint progressive Type-II censoring, which studies the lifetimes of two or more populations simultaneously. In this article, we consider the joint Type-II progressive censoring scheme for two populations when their lifetimes follow Topp-Leone models with unknown common scale parameter but different shape parameters. Classical and Bayesian inferences are studied. Expectation-Maximization (EM) algorithm is implemented for obtaining the maximum likelihood estimators (MLEs) and the associated asymptotic confidence intervals of the unknown parameters. Bayesian inferences are discussed based on a beta-gamma prior for the shape parameters and an incomplete inverse gamma prior for the scale parameter. Importance sampling method is proposed to approximate the Bayes estimates. The associated Bayesian credible intervals are also established. Monte Carlo simulation study is performed to compare the performance of the proposed methods. Finally, a real data set representing two different algorithms for estimating unit capacity factors is analyzed for illustrative purposes. [ABSTRACT FROM AUTHOR]

In this paper, we first develop exact likelihood inference for Laplace distribution based on a generalized Type-I hybrid censored sample (Type-I HCS). We derive explicit expressions for the maximum likelihood estimators (MLEs) of the location and scale parameters. We then derive the joint moment generating function (MGF) of the MLEs, and use it to obtain the exact distributions and moments of the MLEs. Using an analogous approach, we extend the results to a generalized Type-II hybrid censored sample (Type-II HCS) next. Finally, we present a numerical example to illustrate all the results established here. [ABSTRACT FROM AUTHOR]

Accelerated Life Test has been introduced as a tool to aid in obtaining sufficient failure time data of test units quickly and extrapolating lifetime information under use conditions. When the lifetime of units is distributed by the Lindley model, the estimations for the unknown parameters and the reliability function are established based on two frequentist methods and Bayesian method of estimation using Type-II censored data under constant-stress accelerated life test. In the frequentist methods, besides, the conventional likelihood-based estimation, another competitive method, known as the maximum product of spacing method is proposed for estimating the parameters and the reliability function under normal conditions as an alternative approach to the common likelihood method. In Bayesian estimation, both maximum likelihood and maximum product of spacing-based Bayesian estimates are discussed for unknown parameters as well as the reliability function. Moreover, the approximate confidence intervals and highest posterior density credible intervals of the parameters and reliability function are also obtained. Extensive Monte-Carlo simulation studies are conducted to evaluate the performance of the proposed estimates. Finally, to demonstrate the proposed methodology, two real-life accelerated life test data are considered to show the applicabilities of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract Bivariate count data arise in several different disciplines (epidemiology, marketing, sports statistics, etc., to name but a few) and the bivariate Poisson distribution which is a generalization of the Poisson distribution plays an important role in modeling such data. In this article, we consider the inferential aspect of a bivariate Poisson conditionals distribution for which both the conditionals are Poisson but the marginals are typically non-Poisson. It has Poisson marginals only in the case of independence. It appears that a simple iterative procedure under the maximum likelihood method performs quite well as compared with other numerical subroutines, as one would expect in such a case where the MLEs are not available in closed form. In the Bayesian paradigm, both conjugate priors and non-conjugate priors have been utilized and a comparison study has been made via a simulation study. For illustrative purposes, a real-life data set is re-analyzed to exhibit the utility of the proposed two methods of estimation, one under the frequentist approach and the other under the Bayesian paradigm. [ABSTRACT FROM AUTHOR]

In order to guarantee the efficiency of life and reliability test in the case of censored data, and to control the total test time, an adaptive type-II progressive censored scheme is discussed. In this article, the classical estimation methods and Bayesian estimation methods are used to estimate the two unknown parameters, reliability function and hazard function of the Exponentiated Pareto distribution. In addition to the maximum likelihood estimation, the stochastic expectation-maximization (SEM) algorithm is also applied. Under two different loss functions, Lindley's approximation and importance sampling method are used to obtain Bayesian estimates. The Bayesian credible interval is constructed while the Bayesian estimate is evaluated by the Metropolis-Hastings method. The Monte Carlo method is applied to compare the performance of the estimation methods. Then a real life data set is analyzed. Finally, the selection criteria of various estimation methods are proposed. [ABSTRACT FROM AUTHOR]

When the scale parameters and skewness parameters are unknown, we consider the problem of homogeneous test of location parameters in several skew-normal populations. First, the conditional test statistic is constructed and its approximate distribution is proved. Second, we estimate the unknown parameters based on the methods of moment and maximum likelihood estimation. Then we construct the Bootstrap test statistics and generalize the results of Xu from normal population to skew-normal population. Further, the Monte-Carlo simulation results indicate that in terms of controlling the Type I error probability, the Bootstrap test statistic based on the moment estimator performs better than that based on the maximum likelihood estimator. Finally, the above approaches are illustrated with two real examples of gross domestic product and turbine bearing performance. [ABSTRACT FROM AUTHOR]

This article deals with the estimation of the stress–strength reliability model in the event of its strength variable is subjected to the step-stress partially accelerated life test. Inferences for the reliability of such a system are obtained under the assumption that the strength and stress components have one-parameter exponential distributions. Maximum likelihood estimations with their asymptotic and bootstrap confidence intervals are first obtained. Alternatively, the Bayesian estimations with their highest posterior density credible intervals are provided. The performances of the estimators and their corresponding approximate confidence intervals are evaluated using simulation studies. A numerical engineering example is used to illustrate the handled reliability problem. [ABSTRACT FROM AUTHOR]

Joint Type-I progressive hybrid censoring scheme has been proposed to terminate the life-test experiment at maximum time that the experimenter can afford to continue. This article deals with the problem of estimating the two Weibull population parameters with the same shape parameter under joint Type-I progressively hybrid censoring scheme on the two samples using maximum likelihood and Bayesian inferential approaches. Using Fisher information matrix, the two-sided approximate confidence intervals of the unknown quantities are constructed. Under the assumption of independent gamma priors, the Bayes estimators are developed using squared-error loss function. Since the Bayes estimators cannot be expressed in closed forms, hence, Gibbs within Metropolis-Hastings algorithm is proposed to carry out the Bayes estimates and also to construct the corresponding credible intervals. Moreover, some popular joint censoring plans are generalized and can be obtained as a special cases from our results. Monte Carlo simulations are performed to assess the performance of the proposed estimators. To determine the optimal progressive censoring plan, two different optimality criteria are considered. Finally, to show the applicability of the proposed methods in real phenomenon, a real-life data set is analyzed. [ABSTRACT FROM AUTHOR]

The progressive censoring plan has achieved significant recognition in recent years. Its generalization, termed as the joint progressive censoring scheme, has also received numerous researchers' attention. Mondal and Kundu proposed a balanced two sample type-II progressive censoring scheme, in which one practices life test in order to compare the lifetime of the products, produced from various lines in an identical experimental environment. This study concentrates on the estimation problem of lifetime Lindley distributions under the classical paradigm within the balanced two samples type-II progressive censoring framework. A simulation study has been conducted to evaluate the considered estimation procedures' performance through the mean square error and the average length of the asymptotic confidence interval. The optimal censoring scheme is also formulated based on the criteria that rely on Fisher's information. Finally, for an illustration purpose, a real-life application is presented. [ABSTRACT FROM AUTHOR]

The exponential model is the simplest among all lifetime distribution models and it possesses a constant failure rate. Here we propose a new class of lifetime distribution having decreasing failure rate which we developed through compounding exponential distribution with the positive hyper-Poisson distribution. We investigate some of its statistical properties and employed various methods of estimation for estimating the parameters of the distribution along with certain test procedures. All the procedures discussed in the paper are illustrated with the help of real-life data sets. Further, a brief simulation study is conducted for examining the performance of the estimators of the parameters of the distribution. [ABSTRACT FROM AUTHOR]

Abstract A generalization of some well-known probability distributions (viz., Weibull, exponential, gamma, Maxwell, and Chi-square) is introduced using the concept of weighted probability distributions. The introduced model is named Kth-order equilibrium Weibull distribution (KEWD). Various properties of the new distribution are studied in detail. One of the important properties of KEWD is that its hazard rate shows increasing, decreasing, and constant behavior. It is also shown that the new model belongs to the log exponential family. Various ordering relations of the KEWD are studied in comparison with the baseline model, i.e. Weibull distribution. Parameters are estimated using the concept of the maximum likelihood estimation technique. Using the Anderson–Darling test statistic, a simulation study is carried out to analyze the asymptotic normality behavior of maximum likelihood estimators. The behaviors of bias and mean square error are observed with the increase in sample size. The applications of new distribution are illustrated through its fitting to some incorporated real-life data sets. Finally, a comparison is made between KEWD, its sub-models, and some other introduced extensions of Weibull distribution in terms of fitting using the Akaike information criterion (AIC). [ABSTRACT FROM AUTHOR]

Based on record statistics from three-parameter modified Weibull distribution, we consider the problem of estimating the unknown parameters using Bayesian and non-Bayesian approaches. Under a continuous-discrete joint prior distribution, Bayesian estimators and confidence intervals for the shape and scale parameters involved in the underlying model are obtained. In addition, maximum likelihood prediction and Bayesian prediction (either point or interval) of future record statistics based on an informative set of records are developed. Data analyses involving records extracted from a machine used to measure burr and times to breakdown of an insulating fluid between electrodes have been performed. Finally, Monte Carlo simulations are performed to compare the methods developed here. [ABSTRACT FROM AUTHOR]

In this article, we provide a consistent method of estimation for the parameters of a three-parameter generalized exponential distribution which avoids the problem of unbounded likelihood function. The method is based on a maximum likelihood estimation of the shape parameter, which uses location and scale invariant statistic, originally proposed by Nagatsuka et al. (A consistent method of estimation for the three-parameter weibull distribution, Computational Statistics & Data Analysis 58:210–26). It has been shown that the estimators are unique and consistent for the entire range of the parameter space. We also present a Monte-Carlo simulation study along with the comparisons with some prominent estimation methods in terms of the bias and root mean square error. For the illustration purpose, the data analysis of a real lifetime data set has been reported. [ABSTRACT FROM AUTHOR]

In this paper, stress-strength model is studied for an inverted exponential Rayleigh distribution (IERD) when the latent failure times are progressively Type-II censored. When both strength and stress random variables follow common IERD scale parameters, the maximum likelihood estimate of stress-strength reliability (SSR) is established and the associated approximate confidence interval is also constructed using the asymptotic distribution theory and delta method. By constructing pivotal quantities, another alternative generalized estimates for SSR are also proposed for comparison. Moreover, when there are arbitrary strength and stress parameters, likelihood and generalized pivotal based estimates are also presented. In addition, testing problem is gave for comparing the equality of different strength and stress parameters. Finally, simulation study and a real data example are provided for illustration. [ABSTRACT FROM AUTHOR]

Competing risk analysis of time to failure data is preferred when failure of the unit occurs due to any one of several mutually exclusive causes. Masked data refer to the competing risk data with missing cause of failure. Masking in such data may depend on cause of failure or time to failure of the unit or may be independent of both. In this paper, we discuss competing risk models based on Lindley distribution assuming masking to be symmetric, cause dependent and time dependent. We consider maximum likelihood as well as Bayesian approaches for point and interval estimation of model parameters. We perform extensive simulation study to observe performance of various estimators. Finally, we analyze a real life masked data of cancer patients and select the best masking model for the same. [ABSTRACT FROM AUTHOR]

Abstract In this work, we present classical and Bayesian inferential methods based on samples in the presence of progressive type-II censoring under the Very Flexible Weibull (VFW) distribution. The considered distribution is relevant because it is an alternative to traditional non-flexible distributions and also to some flexible distributions already known in the literature, keeping the low amount of two parameters. In addition, studying it in a context of progressive censoring allows attesting to its applicability in data modeling from various areas of industry and technology that can use this censoring methodology. We obtain the maximum likelihood estimators of the model parameters, as well as their asymptotic variation measures. We propose the use of Markov chain Monte Carlo methods for the computation of Bayes estimates. A simulation study is carried out to evaluate the performance of the proposed estimators under different sample sizes and progressive type-II censoring schemes. Finally, the methodology is illustrated through three real data sets. [ABSTRACT FROM AUTHOR]

Abstract We study estimation on parameter-driven models for time series of counts. This class of models follows the structure of a generalized linear model in which the serial dependency is included in the model by the link function through a time-dependent latent process. The likelihood function for this class of models commonly cannot be calculated explicitly and computationally intensive methods like importance sampling and Markov chain Monte Carlo are used to estimate the model parameters. Here, we propose a simple and fast estimation procedure in a wide class of models that accommodate both discrete and continuous data. The maximum likelihood methodology is used to obtain the parameter estimates for the models under study. The simplicity of the procedure allows for build bootstrap confidence intervals for the hyperparameters and latent states of parameter-driven models. We perform extensive simulation studies to verify the asymptotic behavior of the parameter estimates, as well as present application of the proposed procedure through set of real data. [ABSTRACT FROM AUTHOR]

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]

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]

The Poisson regression model (PRM) aims to model a counting variable y, which is usually estimated by using maximum likelihood estimation (MLE) method. The performance of MLE is not satisfactory in the presence of multicollinearity. Therefore, we propose a Poisson James-Stein estimator (PJSE) as a solution to the problems of inflated variance and standard error of MLE with multicollinear explanatory variables. For assessing the superiority of proposed estimator, we present a theoretical comparison based on the matrix mean squared error (MMSE) and scalar mean squared error (MSE) criterions. A Monte Carlo simulation study is performed under different conditions in order to investigate the performance of the proposed estimator where MSE is considered as an evaluation criterion. In addition, an aircraft damage data is also considered to assess the superiority of proposed estimator. Based on the results of simulation and real data application, it is shown that the PJSE outperforms the classical MLE and other biased estimation methods in a sense of minimum MSE criterion. [ABSTRACT FROM AUTHOR]

Mixed fractional Brownian motion is a linear combination of Brownian motion and independent Fractional Brownian motion that is extensively used for option pricing. The consideration of the mixed process is able to capture the long–range dependence property that financial time series exhibit. This paper examines the problem of deriving simultaneously the estimators of all the unknown parameters for a model driven by the mixed fractional Brownian motion using the maximum likelihood estimation method. The consistency and asymptotic normality properties of these estimators are provided. The performance of the methodology is tested on simulated data sets, and the outcomes illustrate that the maximum likelihood technique is efficient and reliable. An empirical application of the proposed method is also made to the real financial data from four Nordic stock market indices. [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 article, we consider estimating the parameters, reliability function R(t) and failure rate function H(t) of the two-parameter bathtub-shaped distribution introduced by Chen (2000) based on the progressive first-failure censored sample. The maximum likelihood estimators and Bayes estimators under squared error loss function are derived. We obtain the asymptotic confidence intervals for the parameters using the observed Fisher information matrix. The parametric bootstrap confidence intervals of reliability characteristics are also proposed. Lindley approximation procedure is adopted to establish Bayes estimates. Furthermore, we conduct Monte Carlo simulation to compare the behaviors of different methods. A real data set is analyzed to illustrate the proposed methods. [ABSTRACT FROM AUTHOR]

Generalized weighted exponential (GWE) distributions are a natural generalization of weighted exponential distributions. This paper attempts to revisit the GWE distribution in order to address the main inferential aspects of this distribution, such as the maximum likelihood estimators of the unknown parameters and their corresponding asymptotic confidence intervals, that vanished in previous works. Also, it develops some new distributional results about the GWE distribution and provides more interesting closed form expressions for previously presented results. A simulation study and a real world application are also worked out to assess the maximum likelihood estimators and to illustrate the theory. [ABSTRACT FROM AUTHOR]

In this paper, a univariate finite mixed generalized normal distribution (MixGND) is proposed. First, we derive some probabilistic properties including hazard rate function, characteristic function, kurtosis and skewness, for a mixture of two generalized normal distributions. In particular, we use a geometric analysis and numerical simulation technique to study the monotonicity of skewness and kurtosis from prescribing corresponding parameters. Then moment estimation and maximum likelihood estimation of parameters are also given. To use the maximum likelihood estimation (MLE) method, an expectation conditional maximization (ECM) algorithm is proposed to estimate and numerically simulate seven parameters of a two-component MixGND under the same variance and heteroscedasticity. By using data sets of the S&P 500 and Shanghai Stock Exchange Composite Index (SSEC), we compare goodness-of-fit performance between the mixture of two generalized normal distributions and the mixture of two normal distributions. The empirical analysis results show that the former better describes the heavy-tailed and leptokurtic characteristics of the daily returns. [ABSTRACT FROM AUTHOR]

In this paper, we empirically study models for pricing Italian sovereign bonds under a reduced form framework, by assuming different dynamics for the short-rate process. We analyze classical Cox-Ingersoll-Ross and Vasicek multi-factor models, with a focus on optimization algorithms applied in the calibration exercise. The Kalman filter algorithm together with a maximum likelihood estimation method are considered to fit the Italian term-structure over a 17-year horizon, including the global financial crisis, the euro area sovereign debt crisis and the Italian political turmoil in 2018. Analytic formulas for the gradient vector and the Hessian matrix of the likelihood function are provided. [ABSTRACT FROM AUTHOR]

In this study, a Shewhart type control chart, namely V R chart, has been proposed to monitor a process that follows Rayleigh distribution. The proposed V R chart is implemented to monitor the single scale parameter of the Rayleigh distributed process. We have studied the proposed chart under two type of control limits namely probability and L -sigma limits. The performance of the proposed chart has been assessed by using power function. In addition, we have investigated run length properties including average run length (ARL), standard deviation of run length (SDRL) and median run length (MDRL). The analysis of run length profile reveals that the proposed VRchart outperforms the existing charts including the traditional Shewhart control chart and V control charts under Rayleigh distribution. The construction process for the newly proposed chart has been demonstrated using a simulated data. Finally, a real application of the proposed V R chart, along with the existing V chart, is presented that evaluates the strength of glass fiber in a manufacturing process. [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]

Asymptotic distribution theory for maximum likelihood estimators under fixed alternative hypotheses is reported in the literature even though the power of any realistic test converges to one under fixed alternatives. Under fixed alternatives, authors have established that nuisance parameter estimates are inconsistent when sample size re-estimation (SSR) follows blinded randomization. These results have helped to inhibit the use of SSR. In this paper, we argue for local alternatives to be used instead of fixed alternatives. We treat unavailable treatment assignments in blinded experiments as missing data and rely on single imputation from marginal distributions to fill in for missing data. With local alternatives, it is sufficient to proceed only with the first step of the EM algorithm mimicking imputation under the null hypothesis. Then, we show that blinded and unblinded estimates of the nuisance parameter σ θ 2 are consistent, and re-estimated sample sizes converge to their locally asymptotically optimal values. This theoretical finding is confirmed through Monte-Carlo simulation studies. Practical utility is illustrated through a multiple logistic regression example. We conclude that, for hypothesis testing with a predetermined minimally clinically relevant local effect size, both blinded and unblinded SSR procedures lead to similar sample sizes and power. [ABSTRACT FROM AUTHOR]

In many practical problems relate to progressively Type-II censored sampling plans, not only an experiment process determines inevitably to use random removals but also a fixed removals assumption may be cumbersome to analyze some results of statistical inference. This paper investigates the estimation problem when lifetimes are the two-parameter Lindley distributed and are collected under two removal patterns based on the uniform discrete distribution and the binomial distribution. The maximum likelihood estimations (MLEs) of parameters are obtained by a derivative-free optimization method and without applying the logarithm of the likelihood function. Furthermore, we propose a method for starting values of optimization to obtain the MLEs and compare numerically their bias, variance, covariance and mean squared error under the two different removal plans. Then, the expected times are discussed and compared numerically under the two approaches of generating random removals. Finally, the optimal progressive Type-II censoring scheme is provided based on the measure of the smallest expected experiment time. [ABSTRACT FROM AUTHOR]

In this paper, a competing risks model based on a generalized progressive hybrid censoring is considered. When the latent lifetime distributions of failure causes are exponential distributed and partially observed, maximum likelihood estimates for unknown parameters are established and the associated asymptotic confidence interval estimates are provided by using approximate theory via the observed Fisher information matrix. Moreover, Bayes point estimates and the highest posterior density credible intervals of unknown parameters are also considered, and the importance sampling procedure is used to approximate corresponding estimates. Finally, a real-life example and simulation study are presented for illustration. [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]

Gamma, lognormal and Weibull distributions are most commonly used in modeling asymmetric data coming from the areas of life testing and reliability engineering. In this study, we deal with the problem of selecting one of these distributions for a given data set which is consistent with the geometric process (GP) model according to T -statistic based on the ratio of the maximized likelihood (RML). First, we show that T -statistic performs better than Kolmogorov- Smirnov (KS), mean square error (MSE) and maximum percentage error (MPE) based on extensive simulation study. Then, by using the T-statistic, we determine the distributions of ten real data sets shown to be consistent with the GP model by Lam et al. (2004). After validating the distribution for these data sets, we calculate the estimators of the parameters by using the suitable method given in Lam and Chan (1998), Chan, Lam, and Leung (2004) or Aydoğdu, Şenoğlu, and Kara (2010). Then, we plot observed and the fitted values of the interarrival and arrival times for comparison. [ABSTRACT FROM AUTHOR]

In this paper, motivated by a real data example about borderline overian tumors, we study a two-dimension dynamic panel models with confounding individual effect for modeling binary panel data. We propose using the maximum likelihood estimation method to estimate the model parameters. The properties of the maximum likelihood estimators are studied. The performance of the proposed estimation method is studied by using a Monte Carlo simulation study. The proposed model and estimation methods are illustrated by the real data example. [ABSTRACT FROM AUTHOR]

In this paper, it is introduced a new parametric distribution to be used in multivariate lifetime data analysis as an alternative for the use of some existing multivariate parametric models as the popular multivariate normal distribution which is the most widely used model assumed in the analysis of continuous multivariate data. Although the normal multivariate distribution has univariate marginal normal probability distributions and simple interpretations for all their parameters, it may not be well fitted by many data sets, especially in survival data applications, usually considering logarithm transformed data. In many cases the use of parametric multivariate discrete models could be more appropriate for the data analysis. In this paper, it is introduced a generalization of the bivariate Basu-Dhar geometric distribution to a trivariate case applied to count data. Some properties of this trivariate geometric distribution, including its marginal probability distributions, order statistics distributions, the probability generating function and some simulation studies are presented. It is also presented some discussion on an extension of the trivariate case for the multivariate case. Classical and Bayesian inferences are presented assuming censored or uncensored observations. To illustrate the proposed methodology, two applications with real lifetime data are considered as examples. [ABSTRACT FROM AUTHOR]