Journal of Iranian Statistical Society
Volume:21 Issue: 1, Spring 2022

We propose a nonparametric estimator for the residual entropy function based on length-biased data. Some asymptotic results have been proved. The strong consistency and asymptotic normality of the proposed estimator are established under suitable regularity conditions. Monte Carlo simulation studies are carried out to evaluate the performance of the estimator using the bias and mean-squared error. A real data set is considered, and we show that the data follow a length-biased distribution. Moreover, the proposed estimator yields a better value for the estimated residual entropy in comparison to the competitor estimator.

Fishing industry has always been an economic motor in many countries around the world, but the fisheries production faces a lot of uncertainty and instability due to the complex factors involved in its operations. In this article, we consider the problem of modeling Chile fishing data using environmental exogenous variables with generalized autoregressive conditional heteroskedasticity (GARCH-X) type models. We carried out this by proposing an ARMA type model for the mean with GARCH-X noise. First, the ARMA, GARCH and GARCH-X models are briefly introduced and the data is described. The exogenous variables are selected from a group of environmental and climatic indicators by correlational analysis. Then, ARMA GARCH and ARMA GARCH-X models with exogenous variables are fitted and compared by information criteria and classical error measures, and stability of its parameters are checked. The statistical tests and comparisons evidenced that a model with inclusion of external variables in mean and variance with the ARMA GARCH-X specification performed better and adjusted the observed values more rigorously. Finally, some conclusions and possible refinations of the applied techniques are given.

This article introduces a two-step calibration technique for the inverse relationship between study variable and auxiliary variable along with the double use of the auxiliary variable. In the first step, the calibration weights and design weights are set proportional to each other for a given sample. While in the second step, the constant of proportionality is to be obtained on the basis of some different objectives of the investigation viz. bias reduction or minimum Mean Squared Error (MSE) of the proposed estimator. Many estimators based on inverse relationship between $x$ and $y$ have been already developed and are considered to be special cases of the proposed estimator. Properties of the proposed estimator is discussed in details. Moreover, a simulation study has also been conducted to compare the performance of the proposed estimator under Simple Random Sampling Without Replacement (SRSWOR) and Lahiri-Midzuno (L-M) sampling design in terms of percent relative bias and MSE. The benefits of two-step calibration estimator are also demonstrated using real life data.

Nair and Rajesh (2000) introduced the geometric vitality function, which explains the failure pattern of components or systems based on the component's geometric mean of the remaining lifetime. Recently quantile-based studies have found greater interest among researchers as an alternative method of measuring the uncertainty of a random variable. The quantile-based measures possess some unique properties to the distribution function approach. The present paper introduces a quantile-based past geometric vitality function of order statistics and its properties. Finally, we provide an application for the new measure based on some distributions which are useful in lifetime data analysis.

The transformer network is a deep learning architecture that uses self-attention mechanisms tocapture the long-term dependencies of a sequential data. The Poisson-Lee-Carter model, introduced to predict mortality rate, includes the factors of age and the calendar year, which is a time-dependent component. In this paper, we use the transformer to predict the time-dependent component in the Poisson-Lee-Carter model. We use the real mortality data set of some countries to compare the mortality rate prediction performance of the transformer with that of the long short-term memory (LSTM) neural network, the classic ARIMA time series model and simple exponential smoothing method. The results show that the transformer dominates or is comparable to the LSTM, ARIMA and simple exponential smoothing method.

This paper is concerned with the estimation problem in semiparametric linear mixed models when some of the covariates are measured with errors. The authors proposed the corrected score function estimators for the parametric and non parametric components. The resulting estimators are shown to be consistent and asymptotically normal. An iterative algorithm is proposed for estimating the parameters. Asymptotic normality of the estimators is also derived. Finite sample performance of the proposed estimators is assessed by Monte Carlo simulation studies. We further illustrate the proposed procedures by an application.

Lifetime data has several applications in different fields such as Biology and Engineering. Failures for this type of data may occur due to several causes. In real world, causes of failures are interacting together which violates the independency assumption. Once dependency between failures is satisfied, bivariate families should be used to analyze the data. In literature, the majority of studies handle the case when data come from one source. However, in real life, data could come from different sources. One way to analyze data from different sources together and reduce the time and cost of the experiment is joint type-II censoring. To the best of our knowledge, joint type-II censoring was not yet derived using bivariate lifetime distributions. In this paper, we derive the likelihood function of joint type-II censoring using bivariate family in the presence of dependent competing risks. A simulation study is performed and two real datasets are analyzed.

In this paper, we consider the problem of estimating the unknown parameters of an exponentiated Weibull distribution when the data are observed in the presence of progressively Type II censoring. We observed that the maximum likelihood estimators do not have a closed form, and so require a numerical technique to compute, further the implementation of the EM algorithm still requires the numerical techniques. So we employ the stochastic expectation-maximization (SEM) algorithm to estimate the model parameters and further to construct the associated asymptotic confidence intervals of the unknown parameters. Moreover, under Bayesian approach, we consider symmetric and asymmetric loss functions and compute the Bayesian estimates using the Lindley’s approximation and Gibbs sampler together with Metropolis Hastings algorithm. The highest posterior density (HPD) credible intervals are also constructed. The behavior of suggested estimators is assessed using a simulation study. Finally, a real life example is considered to illustrate the application and development of the inference methods.