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Showing 20 results for Subject:
Jalal Chachi, Gholamreza Hesamian,
Volume 8, Issue 1 (9-2014)
Abstract
In this paper, we deal with modeling crisp input-fuzzy output data by constructing a MARS-fuzzy regression model with crisp parameters estimation and fuzzy error terms for the fuzzy data set. The proposed method is a two-phase procedure which applies the MARS technique at phase one and an optimization problem at phase two to estimate the center and fuzziness of the response variable. A realistic application of the proposed method is also presented in a hydrology engineering problem. Empirical results demonstrate that the proposed approach is more efficient and more realistic than some traditional least-squares fuzzy regression models.
Shahram Yaghoubzadeh, Ali Shadrokh, Masoud Yarmohammadi,
Volume 9, Issue 1 (9-2015)
Abstract
In this paper, we introduce a new five-parameters distribution with increasing, decreasing, bathtub-shaped failure rate, called as the Beta Weibull-Geometric (BWG) distribution. Using the Sterling Polynomials, the probability density function and several properties of the new distribution such as its reliability and failure rate functions, quantiles and moments, Renyi and Shannon entropies, moments of order statistics, mean residual life, reversed mean residual life are obtained. The maximum likelihood estimation procedure is presented in this paper. Also, we compare the results of fitting this distribution to some of their sub-models, using to a real data set. It is also shown that the BWG distribution fits better to this data set.
Shahram Yaghoobzadeh,
Volume 11, Issue 2 (3-2018)
Abstract
In this paper, the maximum liklihood estimation, unbiased estimations with minimum variance, percentile estimation, best percentile estimation single-observation estimation and the best percentile estimation two-observations in class which are based on order statistics are calculated in two sections for probability density and cumulative distribution functions of the beta Weibull geometric distribution, specially with bathtub-shaped and unimodal failure rate which are useful for modeling of data related to reliability and lifetime. Furthermore, through the simulation method of Monte Carlo and calculation of average square of errors of estimators, they are subjected to comparisons ultimately, the desirable estimator in each section is determined.
Shahram Yaghoobzadeh Shahrastani,
Volume 12, Issue 1 (9-2018)
Abstract
In this paper, based on generalized order statistics the Bayesian and maximum liklihood estimations of the parameters, the reliability and the hazard functions of Gompertz distribution are investigated. Specializations to Bayesian and maximum liklihood estimators, some lifetime parameters of progressive II censoring and record values are obtained. Also by using two real data sets and simulated data accurations of different estimates of the parameters are compared. Next the Bayesian and maximum liklihood estimates of the Gompertz distribution are compared with Weibull and Lomax distrtibutions.
Ali Shadrokh, Shahram Yaghoobzadeh, Masoud Yarmohammadi,
Volume 12, Issue 1 (9-2018)
Abstract
In this article, with the help of exponentiated-G distribution, we obtain extensions for the Probability density function and Cumulative distribution function, moments and moment generating functions, mean deviation, Racute{e}nyi and Shannon entropies and order Statistics of this family of distributions. We use maximum liklihood method of estimate the parameters and with the help of a real data set, we show the Risti$acute{c}-Balakrishnan-G family of distributions is a proper model for lifetime distribution.
Ali Shadrokh, Shahram Yaghoobzadeh Shahrastani,
Volume 13, Issue 2 (2-2020)
Abstract
In this study, the E-Bayesian and hierarchical Bayesian for stress-strength, when X and Y are two independent Rayleigh distributions with different parameters were estimated based on the LINEX loss function. These methods were compared with each other and with the Bayesian estimator using Monte Carlo simulation and two real data sets.
Ali Sakhaei, Parviz Nasiri,
Volume 13, Issue 2 (2-2020)
Abstract
The non-homogeneous bivariate compound Poisson process with short term periodic intensity function is used for modeling the events with seasonal patterns or periodic trends. In this paper, this process is carefully introduced. In order to characterize the dependence structure between jumps, the Levy copula function is provided. For estimating the parameters of the model, the inference for margins method is used. As an application, this model is fitted to an automobile insurance dataset with inference for margins method and its accuracy is compared with the full maximum likelihood method. By using the goodness of fit test, it is confirmed that this model is appropriate for describing the data.
Shahram Yaghoobzadeh,
Volume 14, Issue 1 (8-2020)
Abstract
In this study, the E-Bayesian estimation of the reliability parameter, R = P(Y < X < Z), when X, Y and Z are three independent inverse Rayleigh distribution with different parameters, were estimated based on ranked set sampling method. To assess the efficiency of the obtained estimates, we compute the average absolute bias and relative efficiency of the derived estimates and compare them with those based on the corresponding simple random sample through Monte Carlo simulations. Also, E-Bayesian estimation of R is compared with its maximum likelihood estimation in each method. Finally, three real data sets are used to analyze the estimation methods.
Reza Zarei, ,
Volume 14, Issue 2 (2-2021)
Abstract
In this paper, the Bayesian and empirical Bayesian approaches studied in estimate the multicomponent stress–strength reliability model when the strength and stress variables have a generalized Rayleigh distribution with different shape parameters and identical scale parameter. The Bayesian, empirical Bayesian and maximum likelihood estimation of reliability function is obtained in the two cases known and unknown of scale parameter under the mean squared error loss function. Then, these estimators are compared empirically using Monte Carlo simulation and two real data sets.
Zahra Khadem Bashiri, Ali Shadrokh, Masoud Yarmohammadi,
Volume 15, Issue 1 (9-2021)
Abstract
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.
Ehsan Golzade Gervi, Parviz Nasiri, Mahdi Salehi,
Volume 15, Issue 1 (9-2021)
Abstract
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.
Parviz Nasiri, Raouf Obeidi,
Volume 16, Issue 1 (9-2022)
Abstract
This paper presents the inverse Weibull-Poisson distribution to fit censored lifetime data. The parameters of scale, shape and failure rate are considered in terms of estimation and hypothesis testing, so the parameters are estimated under the type-II of censorship using the maximum likelihood and Bayesian methods. In Bayesian analysis, the parameters are estimated under different loss functions. The simulation section presents the symmetric confidence interval and HPD, and the estimators are compared using statistical criteria. Finally, the model's goodness of fit is evaluated using an actual data set.
Mr Reza Zabihi Moghadam, Dr Masoud Yarmohammadi, Dr Hossein Hassani, Dr Parviz Nasiri,
Volume 16, Issue 2 (3-2023)
Abstract
The Singular Spectrum Analysis (SSA) method is a powerful non-parametric method in the field of time series analysis and has been considered due to its features such as no need to stationarity assumptions or a limit on the number of collected observations. The main purpose of the SSA method is to decompose time series into interpretable components such as trend, oscillating component, and unstructured noise. In recent years, continuous efforts have been made by researchers in various fields of research to improve this method, especially in the field of time series prediction. In this paper, a new method for improving the prediction of singular spectrum analysis using Kalman filter algorithm in structural models is introduced. Then, the performance of this method and some generalized methods of SSA are compared with the basic SSA using the root mean square error criterion. For this comparison, simulated data from structural models and real data of gas consumption in the UK have been used. The results of this study show that the newly introduced method is more accurate than other methods.
Mahdieh Mozafari, Mohammad Khanjari Sadegh, , Gholamreza Hesamian,
Volume 17, Issue 1 (9-2023)
Abstract
In this paper, some reliability concepts have been investigated based on the α-pessimistic and its relationship with the α-cut of a fuzzy number. For this purpose, if the lifetime distribution of the system components is known, using the definition of the scale fuzzy random variable, based on α-pessimistic, some reliability criteria have been investigated. Also, suppose the lifetime distribution of the components is unknown or only the fuzzy observations of the lifetime of the features are available. In that case, the empirical distribution function of the fuzzy data is used to estimate the reliability, and some examples are provided to illustrate the results.
Shahrastani Shahram Yaghoobzadeh,
Volume 17, Issue 1 (9-2023)
Abstract
In this article, it is assumed that the arrival rate of customers to the queuing system M/M/c has an exponential distribution with parameter $lambda$ and the service rate of customers has an exponential distribution with parameter $mu$ and is independent of the arrive rate. It is also assumed that the system is active until time T. Under this stopping time, maximum likelihood estimation and bayesian estimation under general entropy loss functions and weighted error square, as well as under-informed and uninformed prior distributions, the system traffic intensity parameter M/M/c and system stationarity probability are obtained. Then the obtained estimators are compared by Monte Carlo simulation and a numerical example to determine the most suitable estimator.
Miss. Mahdieh Mozafari, Dr. Mohammad Khanjari Sadegh, Dr. Mohammad Ghasem Akbari, Dr. Gholamreza Hesamian,
Volume 18, Issue 1 (8-2024)
Abstract
In this paper, fuzzy order statistics are expressed based on the concept of α-value, and some of its applications in reliability have been examined. For this purpose, if the lifetime distribution of the system components is known, some of the reliability criteria of the $i$th order statistic using the definition of a fuzzy random variable based on the α-value have been investigated. Also, if the lifetime distribution of the components is unknown or only the fuzzy observations of the lifetime of the components are available, the empirical distribution function of the fuzzy data is used to estimate the reliability based on ordinal statistics, and examples are provided to illustrate the results.
Hossein Mohammadi, Mohammad Ghasem Akbari, Gholamreza Hesamian,
Volume 18, Issue 1 (8-2024)
Abstract
First, this article defines a meter between fuzzy numbers using the support function. Then, based on the support function, the concepts of variance, covariance, and correlation coefficient between fuzzy random variables are expressed, and their properties are investigated. Then, using the above concepts, the p-order fuzzy autoregressive model is introduced based on fuzzy random variables, and its properties are investigated. Finally, to explain the problem further, examples will be presented and compared with similar models using some goodness of fit criteria.
Ms. Samira Taheri, Dr Mohammad Ghasem Akbari, Dr Gholamreza Hesamian,
Volume 18, Issue 1 (8-2024)
Abstract
In this paper, based on the concept of $alpha$-values of fuzzy random variables, the fuzzy moving average model of order $q$ is introduced. In this regard, first, the definitions of variance, covariance, and correlation coefficient between fuzzy random variables are presented, and their properties are investigated. In the following, while introducing the fuzzy moving average model of order $q$, this model's autocovariance and autocorrelation functions are calculated. Finally, some examples are presented for the obtained results.
Dr Adeleh Fallah,
Volume 18, Issue 1 (8-2024)
Abstract
In this paper, non-parametric inference is considered for $k$-component coherent systems, when the system lifetime data is progressively type-II censored. In these coherent systems, it is assumed that the system structure and system signature are known. Based on the observed progressively type-II censored, non-parametric confidence intervals are calculated for the quantiles of component lifetime distribution. Also, tolerance limits for component lifetime distribution are obtained. Non-parametric confidence intervals for quantiles and tolerance limits are obtained based on two methods, distribution function method and W mixed matrix method. Two numerical example is used to illustrate the methodologies developed in this paper.
, Roshanak Zaman,
Volume 18, Issue 2 (2-2025)
Abstract
In this paper, the prediction of the lifetime of k-component coherent systems is studied using classical and Bayesian approaches with type-II censored system lifetime data. The system structure and signature are assumed to be known, and the component lifetime distribution follows a half-logistic model. Various point predictors, including the maximum likelihood predictor, the best-unbiased predictor, the conditional median predictor, and the Bayesian point predictor under a squared error loss function, are calculated for the coherent system lifetime. Since the integrals required for Bayes prediction do not have closed forms, the Metropolis-Hastings algorithm and importance sampling methods are applied to approximate these integrals. For type-II censored lifetime data, prediction interval based on the pivotal quantity, prediction interval HCD, and Bayesian prediction interval are considered. A Monte Carlo simulation study and a numerical example are conducted to evaluate and compare the performances of the different prediction methods.
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