Journal of Statistical Sciences

On The Applications Of Total Time on Test Transform In Reliability

Mohammad Amini

In this article, the total time on test (TTT) transformation and its major properties are investigated. Then, the relationship between the TTT transformation and some subjects in reliability theory is expressed. The TTT diagram is also drawn for some well-known lifetime distributions, and a real-data analysis is performed based on this diagram. A new distorted family of distributions is introduced using the distortion function. The statistical interpretation of the new life distribution from the perspective of reliability is provided, and its survival function is derived. Finally, a generalization of the Weibull distribution is introduced using a new distortion function. A real data analysis shows its superiority in fitting in comparison to the traditional Weibull model.

Smallest Confidence Region for the Mean and Standard Deviation of Two-Parameter Uniform Distribution

Mohammad Hossein Poursaeed

In this paper, based on an appropriate pivotal quantity, two methods are introduced to determine confidence region for the mean and standard deviation in a two parameter uniform distribution, in which the application of numerical methods is not mandatory. In the first method, the smallest region is obtained by minimizing the confidence region's area, and in the second method, a simultaneous Bonferroni confidence interval is introduced by using the smallest confidence intervals. By the comparison of area and coverage probability of the introduced methods, as well as, comparison of the width of strip including the standard deviation in both methods, it has been shown that the first method has a better efficiency. Finally, an approximation for the quantile of F
distribution used in calculating the confidence regions in a special case is presented.

Employing Weighted Operators in Ordered Least Deviations Regression Model

Jalal Chachi

This article introduces a new method to estimate the least absolutes linear regression model's parameters, which considers optimization problems based on the weighted aggregation operators of ordered least absolute deviations. In the optimization problem, weighted aggregation of orderd fitted least absolute deviations provides data analysis to identify the outliers while considering different fitting functions simultaneously in the modeling problem. Accordingly, this approach is not affected by outlier observations and in any problem proportional to the number of potential outliers selects the best model estimator with the optimal break-down point among a set of other candidate estimators. The performance and the goodness-of-fit of the proposed approach are investigated, analyzed and compared in modeling analytical dataset and a real value dataset in hydrology engineering at the presence of outliers. Based on the results of the sensitivity analysis, the properties of unbiasedness and efficiency of the estimators are obtained.

On Equivalence of Reliability in Reduction and Redundancy Methods

Majid Chahkandi

Redundancy and reduction are two main methods for improving system reliability. In a redundancy method, system reliability can be improved by adding extra components to some original components of the system. In a reduction method, system reliability increases by reducing the failure rate at all or some components of the system. Using the concept of reliability equivalence factors, this paper investigates equivalence between the reduction and redundancy methods. A closed formula is obtained for computing the survival equivalence factor. This factor determines the amount of reduction in the failure rate of a system component(s) to reach the reliability of the same system when it is improved. The effect of component importance measure is also studied in our derivations.

Bayesian LASSO Regression with Asymmetric Error in High Dimensional

Ali Shadrokh

One of the most critical discussions in regression models is the selection of the optimal model, by identifying critical explanatory variables and negligible variables and more easily express the relationship between the response variable and explanatory variables. Given the limitations of selecting variables in classical methods, such as stepwise selection, it is possible to use penalized regression methods. One of the penalized regression models is the Lasso regression model, in which it is assumed that errors follow a normal distribution. In this paper, we introduce the Bayesian Lasso regression model with an asymmetric distribution error and the high dimensional setting. Then, using the simulation studies and real data analysis, the performance of the proposed model's performance is discussed.

Bayesian Model Averahing in Inverse Gaussian Regression Analysis

Afshin Fallah

This paper considers the Bayesian model averaging of inverse Gaussian regression models for regression analysis in situations that the response observations are positive and right-skewed. The computational challenges related to computing the essential quantities for executing of this methodology and their dominating ways are discussed. Providing closed form expressions for the interested posterior quantities by considering suitable prior distributions is an attractive aspect of the proposed methodology. The proposed approach has been evaluated via a simulation study and its applicability is expressed by using a real example related to the seismic studies.

Using Machine Learning Classification Algorithms in Official Statistics

Zahra Rezaei Ghahroodi

In most surveys, the occupation and job-industry related questions are asked through open-ended questions, and the coding of this information into thousands of categories is done manually. This is very time consuming and costly. Given the requirement of modernizing the statistical system of countries, it is necessary to use statistical learning methods in official statistics for primary and secondary data analysis. Statistical learning classification methods are also useful in the process of producing official statistics. The purpose of this article is to code some statistical processes using statistical learning methods and familiarize executive managers about the possibility of using statistical learning methods in the production of official statistics. Two applications of classification statistical learning methods, including automatic coding of economic activities and open-ended coding of statistical centers questionnaires using four iterative methods, are investigated. The studied methods include duplication, support vector machine (SVM) with multi-level aggregation methods, a combination of the duplication method and SVM, and the nearest neighbor method.

Joint Model of Longitudinal Count and Time to Event Data with Excess Zeros Using the AFT Model: A Case Study of the HIV/ AIDS Dataset

Ehsan Bahrami Samani

This article aims to joint modeling of longitudinal CD4 cells count and time to death in HIV patients based on the AFT model. The modeling of the longitudinal count response, a GLME model under the family of PSD, was used. In contrast, for the TTE data, the parametric AFT model under the Weibull distribution was investigated. These two responses are linked through random effects correlated with the normal distribution. The longitudinal and survival data are then assumed independent, given the latent linking process and any available covariates. Considering excess zeros for two responses and right censoring, presented a joint model that has not yet been investigated by other researchers. The parameters were also estimated using MCMC methods.

Distributions Family of Extended Weibull Combined with Negative Binomial Distribution Truncated at Zero

Nahid Sanjari Farsipour

In this paper, using the extended Weibull Marshall-Olkin-Nadarajah family of distributions, the exponential, modified Weibull, and Gompertz distributions are obtained, and density, survival, and hazard functions are simulated. Next, an algorithm is presented for the simulation of these distributions. For exponential case, Bayesian statistics under squared error, entropy Linex, squared error loss functions and modified Linex are calculated. Finally, the presented distributions are fitted to a real data set.

Comparison of Empirical Bayesian Estimations and Predictions Based on Record Ranked Set Sampling Scheme with Inverse Sampling Scheme

Parviz Nasiri

The empirical Bayes estimation of the exponential distribution parameter under squared error and LINEX loss functions is investigated when the record collects the data ranked set sampling scheme method. Then, point and interval predictions for future record values are studied. The results of this sampling scheme are compared with the products of the inverse sampling scheme. To compare the accuracy of estimators, Bayes risk and posterior risk criteria are used. These point predictors are compared in the sense of their mean squared prediction errors. To evaluate the prediction intervals for both the sampling schemes, the average interval length and coverage probability are computed and compared. In the present study, the hyperparameters are estimated in two methods. By studying the simulation and presenting real data, the estimation methods are compared, and the performance of the introduced schemes is evaluated.

The Suitable Statistical Model Selection for the Wind Speed of Tabriz and Orumiyeh Stations

Meysam Mohammadpour

Wind speed probabilistic distributions are one of the main wind characteristics for the evaluation of wind energy potential in a specific region. In this paper, 3-parameter Log-Logistic distribution is introduced and it compared with six used statistical models for the modeling the actual wind speed data reported of Tabriz and Orumiyeh stations in Iran. The maximum likelihood estimators method via Nelder–Mead algorithm is utilized for estimating the model parameters. The flexibility of proposed distributions is measured according to the coefficient of determination, Chi-square test, Kolmogorov-Smirnov test, and root mean square error criterion. Results of the analysis show that 3-parameter Log-Logistic distribution provides the best fit to model the annual and seasonal wind speed data in Orumiyeh station and except summer season for Tabriz station. Also, wind power density error is estimated for the proposed different distributions.

Bivariate Dependency Analysis using Jeffrey and Hellinger Divergence Measures based on Copula Density Estimation by Improved Probit Transformation

Mahdi Emadi

Divergence measures can be considered as criteria for analyzing the dependency and can be rewritten based on the copula density function. In this paper, Jeffrey and Hellinger dependency criteria are estimated using the improved probit transformation method, and their asymptotic consistency is proved. In addition, a simulation study is performed to measure the accuracy of the estimators. The simulation results show that for low sample size or weak dependence, the Hellinger dependency criterion performs better than Kullback-Libeler and Jeffrey dependency criteria. Finally, the application of the studied methods in hydrology is presented.

Testing the Equality of Regression Coefficients of Panel Models in Several Groups

Ahad Malekzadeh

The panel data model is used in many areas, such as economics, social sciences, medicine, and epidemiology. In recent decades, inference on regression coefficients has been developed in panel data models. In this paper, methods are introduced to test the equality models of the panel model among the groups in the data set. First, we present a random quantity that we estimate its distribution by two methods of approximation and parametric bootstrap. We also introduce a pivotal quantity for performing this hypothesis test. In a simulation study, we compare our proposed approaches with an available method based on the type I error and test power. We also apply our method to gasoline panel data as a real data set.

Analysis of Space-Time Count Data Using the Flexible Gamma-Count Model

Hossein Baghishani

Many of spatial-temporal data, particularly in medicine and disease mapping, are counts. Typically, these types of count data have extra variability that distrusts the classical Poisson model's performance. Therefore, incorporating this variability into the modeling process, plays an essential role in improving the efficiency of spatial-temporal data analysis. For this purpose, in this paper, a new Bayesian spatial-temporal model, called gamma count, with enough flexibility in modeling dispersion is introduced. For implementing statistical inference in the proposed model, the integrated nested Laplace approximation method is applied. A simulation study was performed to evaluate the performance of the proposed model compared to the traditional models. In addition, the application of the model has been demonstrated in analyzing leukemia data in Khorasan Razavi province, Iran.