Search

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 study the estimation of a block covariance matrix with linearly structured off-diagonal blocks. We consider estimation based on the least squares method, which has some drawbacks. These estimates are not always well conditioned and may not even be definite. We propose a new estimation procedure providing a structured positive definite and well-conditioned estimator with good statistical properties. The least squares estimator is improved with the use of a shrinkage method and an additional algebraic approach. The resulting so-called quasi shrinkage estimator is compared with the structured maximum likelihood estimator. [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]

In this paper, studies of competing risks model are considered when the observations are left-truncated and right-censored data. When the failure times of the competing risks are distributed by a generalized inverted exponential model with same scale but different shape parameters with partially observed failure causes, statistical inference for the unknown model parameters is discussed from classical and Bayesian approaches, respectively. Maximum likelihood estimators of the unknown parameters, along with associated existence and uniqueness, are established, and the asymptotic likelihood theory is also used to construct the confidence interval via the observed Fisher information matrix. Moreover, Bayesian estimates and the corresponding highest posterior density credible intervals are also obtained based a flexible Gamma-Beta prior, and a Gibbs sampling technique is constructed to compute associated estimates. Further, under a general practical assumption with order-restriction parameter case, classical and Bayesian estimations are also established under order restriction situations, respectively. Extensive Monte-Carlo simulations are carried out to investigate the performances of our results and two real-life examples are analyzed to show the applicability of the proposed methods. [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]

This paper presents a particle swarm optimization-guided maximum likelihood estimation enabled (MLE) adaptive extended Kalman filter (EKF) with unknown inputs algorithm for estimating the dynamic nonlinear thermal states for an indoor heating ventilation and air conditioning system. The concept of MLE has been introduced to enhance the speed of convergence of the filtering parameters in adaptive EKF. The nonlinear indoor environment has been modelled employing equivalent RC network taking relative humidity into account. At the outset, an EKF-based method accommodating the unknown inputs and an adaptive estimator-based variant of it are developed for estimating the temperature of the walls of a laboratory-scale realistic environment. Subsequently the proposed scheme comes into play to deal with the scenarios associated with undesirable divergence and poor initialization utilizing the metaheuristically adapted optimal regularizer. The proposed technique outperforms the other contemporary state-of-the-art counterparts in terms of mean squared error. [ABSTRACT FROM AUTHOR]

In this paper, a unit inverse Weibull distribution as well as its basic structural properties is proposed. Furthermore, classical inferences for multicomponent reliability are discussed under type-II censoring when stress and strength components have a common parameter. The maximum likelihood estimator of the reliability is obtained and in sequel an asymptotic interval is constructed. Pivotal quantities are constructed and then generalized point and interval estimators are obtained for the reliability. Likelihood and pivotal quantities-based estimations are presented when all parameters are unequal as well. The performance of different estimators is investigated using simulation studies and real-life examples are studied from an application viewpoint. Finally, some concluding remarks are given. [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]

In this paper, interval estimation of the two-parameter exponential distribution based on constant-stress accelerated life test data under Type-II censoring is studied. The life-stress models of the scale and location parameters are assumed to be log-linear. The maximum likelihood estimators of the model parameters are obtained. The exact and approximate confidence intervals for the parameters in the life-stress model of the scale parameter are developed. The generalized confidence intervals for the parameters in the life-stress model of the location parameter, and mean and reliability function at the designed stress level are derived. The performance of the proposed generalized confidence intervals is assessed by the Monte Carlo simulation. Finally, a real example is used to illustrate our methods. [ABSTRACT FROM AUTHOR]

The change point estimation concept is usually useful in time series models. This concept helps to decrease the decision making or production costs by monitoring the stock market and production lines. It is also applied in several fields such as Financing and Quality Control. In this paper, it is assumed that the ARMA (1) model exists between the sample statistics of x ¯ control chart. A maximum likelihood technique is developed to estimate the change point at which the stationary ARMA (1) model changes into a non-stationary process. For the estimation of unknown parameters after the change point, the Smoothing of Dynamic Linear Model has been used based on singular value decomposition. It is assumed that there exists a correlation between sample statistics. Simulation results show the effectiveness of the estimators proposed in this paper to estimate the change point of the stationary state in ARMA (1) model. An example is provided to illustrate the application. [ABSTRACT FROM AUTHOR]

Analysis of jointly censoring schemes has received considerable attention in the last few years. In this paper, maximum likelihood and Bayes methods of estimation are used to estimate the unknown parameters of two Gompertz populations under a joint progressive Type-II censoring scheme. Bayesian estimations of the unknown parameters are obtained based on squared error loss functions under the assumption of independent gamma priors. We propose to apply the Markov Chain Monte Carlo technique to carry out a Bayes estimation procedure. The approximate, bootstrap, and credible confidence intervals for the unknown parameters are also obtained. Also, reliability and hazard rate function of the two Gompertz populations under joint progressive Type-II censoring scheme is obtained and the corresponding approximate confidence intervals. Finally, all the theoretical results obtained are assessed and compared using two real-world data sets and Monte Carlo simulation studies. [ABSTRACT FROM AUTHOR]

Reliability analysis for a multicomponent stress-strength (MSS) model is discussed in this paper. When strength and stress variables follow generalized inverted exponential distributions (GIEDs) with common scale parameters, maximum likelihood estimate of MSS reliability is established along with associated existence and uniqueness, and approximate confidence interval is also obtained in consequence. Additionally, alternative generalized estimates are proposed for MSS reliability based on constructed pivotal quantities, and associated Monte-Carlo sampling is provided for computation. Further, classical and generalized estimates are also established under unequal strength and stress parameter case. For comparison, bootstrap confidence intervals are also provided under different cases. To compare the equivalence of the strength and stress parameters, likelihood ratio testing is presented as a complement. Finally, extensive simulation studies are carried out to assess the performance of the proposed methods, and a real data example is presented for application. The numerical results indicate that the proposed generalized methods perform better than conventional likelihood results. [ABSTRACT FROM AUTHOR]

We develop a novel class of distributions after the exponentiated Weibull family and vtub-shaped failure rate for systems are considered and compounded together. This combined class of distributions can be applied to reliability applications using the data, and we investigate its properties. We study the mathematical properties of combined distributions including order statistics and estimation by maximum likelihood. In addition, we implement an EM algorithm to determine unknown parameters using maximum likelihood estimates, and maximum entropy characterizations are discussed under appropriate constraints. Using maximum likelihood estimation, we obtain point estimates and interval estimation for parameters. We develop a novel approach to measuring the reliability of multi-component systems as well as a single-component system and illustrate the usefulness of the proposed approach. We apply the approach to real data sets and discuss numeric examples to show the statistical properties of the new compounding class of distributions derived in the paper. [ABSTRACT FROM AUTHOR]

Grouped and right-censored (GRC) count data are widely adopted to study some sensitive topics or to collect information from less cognitive respondents in many research fields, such as psychology, sociology, and criminology. However, theoretical analysis of GRC counts is involved due to the co-existence of grouping schemes and right-censoring schemes. Recently, a modified Poisson regression model has been proposed to analyze GRC count data under the framework of maximum likelihood estimation. In this paper, I study the asymptotic properties of the maximum likelihood estimators of GRC counts that can cover the modified Poisson estimator. Existing results on modified Poisson estimators for GRC counts are only applicable to stochastic regressors with strictly positive definite Fisher information matrices. Results in this paper are derived under a milder condition that the information matrix of observations is divergent, which can cover the results for the stochastic case in the almost sure sense. Real data simulations are provided to investigate drug use in America. [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]

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]

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]

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]

Based on the well-known Poisson (P) distribution and the new generalized Lindley distribution (NGLD) developed by using gamma ( α , θ) and gamma ( α − 1 , θ) distributions, a new compound two-parameter Poisson generalized Lindley (TPPGL) distribution is proposed in this paper and thereon systematically explores the mathematical properties. Closed form expressions are assembled for such properties including the probability generating function, moments, skewness, kurtosis, etc. The likelihood-based method is used for estimating the parameters followed by a broad Monte Carlo simulation study. To further motivate the proposed model, a count regression model and a first order integer valued autoregressive process are constructed based on the novel TPPGL distribution. The empirical importance of the proposed models is confirmed through application to four real datasets. [ABSTRACT FROM AUTHOR]

In this paper, two new general families of distributions supported on the unit interval are introduced. The proposed families include several known models as special cases and define at least twenty (each one) new special models. Since the list of well-being indicators may include several double bounded random variables, the applicability for modeling those is the major practical motivation for introducing the distributions on those families. We propose a parametrization of the new families in terms of the median and develop a shiny application to provide interactive density shape illustrations for some special cases. Various properties of the introduced families are studied. Some special models in the new families are discussed. In particular, the complementary unit Weibull distribution is studied in some detail. The method of maximum likelihood for estimating the model parameters is discussed. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Applications to the literacy rate in Brazilian and Colombian municipalities illustrate the usefulness of the two new families for modeling well-being indicators. [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]

This paper proposes a closed-form estimator for the stochastic volatility (SV) model. Compared to the usual maximum likelihood estimation (MLE), which is difficult to perform without appropriate approximations, the proposed method can be easily implemented and does not require the use of any numerical optimizer or starting values for iterations. Moreover, closed-form estimates can be supplied as initial values to MLE, for instance, conducted with a novel Laplace approximation. Denoted by MLE-C, this method consistently outperforms other estimators including the Markov chain Monte Carlo (MCMC). This is confirmed with simulation studies consisting of various combinations of true parameters and sample sizes. Our empirical data include daily returns of S&P 500, Nikkei 225 and DAX 100 over 2011–2020. The SV model estimated by MLE-C almost uniformly beats the popular GARCH counterparty, based on both the in-sample fit and out-of-sample forecasting criteria. Value-at-Risk analyses further demonstrate the capability of the SV model to accurately describe the tail behaviors of negative returns. [ABSTRACT FROM AUTHOR]

The Arellano-Bond estimator is widely used among applied researchers when estimating dynamic panels with fixed effects and predetermined regressors. This estimator might behave poorly in finite samples when the cross-section dimension of the data is small (i.e. small ), especially if the variables under analysis are persistent over time. This paper discusses a maximum likelihood estimator that is asymptotically equivalent to Arellano and Bond (1991) but presents better finite sample behaviour. The estimator is based on an alternative parametrization of the likelihood function introduced in Moral-Benito (2013). Moreover, it is easy to implement in Stata using the xtdpdml command as described in a companion paper published in the Stata Journal, which also discusses further advantages of the proposed estimator for practitioners. [ABSTRACT FROM AUTHOR]

The noterate is a tool for predicting home mortgage rates, it is often skewed and has missing information. The noterate could be affected by incomplete or inaccurate data, thus leading to inaccurate predictions. Financial organizations including mortgage companies or banks need to consider the risk of uncertainty carefully and make a more accurate prediction based on some suitable models. To deal with this situation, in this paper we compared six computational statistical methods, including the ordinary least square model, maximum likelihood estimation, maximum a posterior, bootstrapping, Metropolis-Hastings, and Gibbs sampling method on a mortgage dataset. Based on the k fold cross-validation technique and four metrics including mean absolute error (MAE), mean squared error (MSE), root mean squared error (RMSE), and mean absolute percentage error (MAPE), the bootstrapping method outperforms other methods. In practice, this method is recommended for predicting noterate. [ABSTRACT FROM AUTHOR]

Gompertz distribution is a significant and commonly used lifetime distribution, which plays an important role in reliability engineering. In this paper, we study the statistical inference of Gompertz distribution based on adaptive Type-II hybrid progressive censored schemes. From the perspective of frequentist, we derive the point estimations through the method of maximum likelihood estimation (MLE) and the existence of MLE is proved. Besides MLE, we propose the stochastic EM algorithm to reduce complexity and simplify computing. We also apply the method of Bootstraps (Bootstrap-p and Bootstrap-t) to construct confidence intervals. From Bayesian aspect, the Bayes estimates of the unknown parameters are evaluated by applying the MCMC method, the average length and coverage rate of credible intervals are also carried out. The Bayes inference is based on the squared error loss function and LINEX loss function. Furthermore, a numerical simulation is conducted to assess the performance of the proposed methods. Finally, a real-life example is considered to illustrate the application and development of the inference methods. In summary, the Bayesian method seems to perform the best among all approaches, while other approaches also present different advantages. [ABSTRACT FROM AUTHOR]

In this paper, the Bayesian and non-Bayesian estimation of $$\psi = P(X \gt Y)$$ ψ = P (X > Y) based on the progressively first-failure censored data is considered. The $$X$$ X and $$Y$$ Y are strength and stress random variables and follow the Topp-Leone distributions, respectively. The maximum likelihood and Bayes estimators of $$\psi $$ ψ are derived. The Bayes estimators under generalized entropy loss function are computed using Lindley's approximation and Gibbs sampling methods. Different interval estimates like asymptotic, bootstrap confidence, Bayesian credible, and highest posterior density credible intervals of $$\psi $$ ψ are constructed. Furthermore, a Monte Carlo numerical study is conducted to check the performance of various estimators developed. Finally, an application of algorithm real data is considered for illustrative purposes. [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 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]

The setting considered in this paper concerns a discrete-time multivariate population process under Markov modulation. Our objective is to estimate the model parameters, based on periodic observations of the network population vector. These parameters relate to the arrival, routing and departure processes, but also to the (unobservable) Markovian background process. When opting for the classical likelihood-based approach, the evaluation of the likelihood is problematic. We show however, how an accurate saddlepoint approximation can be used. Numerical experiments illustrate our method and show that even under relatively complicated conditions the parameters are estimated relatively precisely. [ABSTRACT FROM AUTHOR]

Compared with low frequency data, high frequency data exhibit distinct empirical properties, including, for instance, essentially discontinuous evolution paths, time-varying intensities, and self-exciting features. All these make it more challenging to model appropriately the dynamics associated with high frequency data such as order arrival and price formation. To capture more accurately the microscopic structures and properties pertaining to the limit order books, this paper focuses on modeling high frequency data using Hawkes processes. Two models, one with exponential kernels and the other with power-law kernels, are introduced systematically, algorithmized precisely, and compared with each other extensively from various perspectives, including the goodness of fit to the original data and the computational time in searching for the maximum likelihood estimator, with search algorithm being taken into consideration as well. To measure the goodness of fit, a number of quantities are proposed. Studies based on both multiple-trading-day data of one stock and multiple-stock data on one trading day indicate that Hawkes processes with slowly-decaying kernels are able to reproduce the intensity of jumps in the price processes more accurately. The results suggest that Hawkes processes with power-law kernels and their implied long memory nature of self-excitation phenomena could, on the level of microstructure, serve as a realistic model for high frequency data. [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]

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, 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]

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 paper, we introduce six Weibull based mixture distributions to model income data. Several statistical properties of these models are derived and their closed forms are presented. The mixture model parameters are estimated using the maximum likelihood method and their performances are assessed with respect to average income per tax unit data for ten countries using information based criteria approaches as well as graphical observations. In addition, we provide application of these models to two popular inequality measures, the Gini and Bonferroni indexes as well as the common generalized entropy index. Analytic expressions of the poverty measures are given for head-count ratio and poverty-gap ratio. All the mixture models show good fit to the data with close proximity to empirical Gini and Bonferroni indexes in almost all ten countries where the income data sets are studied. [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, inference is discussed for left-truncated and right-censored (LTRC) competing risks data. For modelling the dependent competing risks variables, a flexible bivariate lifetime model is constructed with a class of inverse exponentiated distribution, and associated distribution properties are provided correspondingly. When the LTRC competing risks data is available with partially observed failure causes, a dependent competing risks model is further established. Maximum likelihood estimators of the unknown parameters and the reliability indices are established, and the approximate confidence intervals are also constructed based on asymptotic theory. In addition, Bayesian estimators are obtained based on flexible priors, Markov Chain Monte Carlo sampling approach is also proposed for computing the Bayesian estimates as well as the highest posterior density credible intervals. Finally, simulation studies are carried out to investigate the performances of our results, and a real-life data set is analysed to illustrate the applicability of the proposed methods. [ABSTRACT FROM AUTHOR]

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

In this paper, 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 we introduce a flexible extension of the Gumbel distribution called the odd log-logistic exponentiated Gumbel distribution. The new model was implemented in GAMLSS package of R software and a brief tutorial on how to use this package is presented throughout the paper. We provide a comprehensive treatment of its general mathematical properties. Further, we propose a new extended regression model considering four regression structures. We discuss estimation methods based on censored and uncensored data. Two simulation studies are presented and four real data sets are applied to illustrating the usefulness of the new model. [ABSTRACT FROM AUTHOR]

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

This article compares two asymmetric Gaussian likelihood models and their corresponding estimators. Recently, there has been confusion in the literature regarding these models and (1) whether they are the same, or (2) whether both of them can be used to estimate expectiles. After the comparison, it becomes clear that they are not the same and only one of these models is appropriate for that purpose. The similarity between these models is purely superficial. The historical origin of expectiles has also been disputed: some degree of credit can be shared between two papers. [ABSTRACT FROM AUTHOR]

A complex product is often inspected more than once in a sequential manner to ensure the product’s quality. Based on the number of defects discovered during each round of inspection process, we can estimate the number of defects still remaining in the product. For each defect, the probability that the defect will be detected during each inspection cycle is usually assumed to be a known ‘constant’. However, in many practical situations, some defects are easily detected, while others are much more difficult to identify. In this paper, we propose a ‘beta-geometric’ inspection model in which the heterogeneity in detection probability is described by a beta distribution. In a numerical study, we show that our more realistic inspection model clearly outperforms traditional estimation methods that are based on the assumption of a constant detection probability. [ABSTRACT FROM PUBLISHER]