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Showing 32 results for Estimation
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.
Peyman Amiri Domari, Mehrdad Naderi, Ahad Jamalizadeh,
Volume 12, Issue 2 (3-2019)
Abstract
In order to construct the asymmetric models and analyzing data set with asymmetric properties, an useful approach is the weighted model. In this paper, a new class of skew-Laplace distributions is introduced by considering a two-parameter weight function which is appropriate to asymmetric and multimodal data sets. Also, some properties of the new distribution namely skewness and kurtosis coefficients, moment generating function, etc are studied. Finally, The practical utility of the methodology is illustrated through a real data collection.
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.
Vahid Nekoukhou, Ashkan Khalifeh, Eisa Mahmoudi,
Volume 13, Issue 2 (2-2020)
Abstract
In this paper, we study a three-parameter bivariate distribution obtained by taking Geometric minimum of Rayleigh distributions. Some important properties of this bivariate distribution have been investigated. It is observed that the maximum likelihood estimators of the parameters cannot be obtained in closed forms. We propose to use the EM algorithm to compute the maximum likelihood estimates of the parameters, and it is computationally quite tractable. Based on an extensive simulated study, the effectiveness of the proposed algorithm is confirmed. We also analyze one real data set for illustrative purposes. Finally, we conclude the paper.
Shadi Saeidi Jeyberi, Mohammadreza Zadkarami, Gholamali Parham,
Volume 14, Issue 1 (8-2020)
Abstract
In this paper, Bayesian fuzzy estimator is obtained first, for the fuzzy data based on the probability prior distribution and afterward based on the possible model and the possibility of a prior distribution. Considering the effect of the membership functions on the fuzzy and possibility Bayesian estimators, a membership function that gives the optimal fuzzy and possibility Bayesian estimators will be introduced for the data. The optimality of the new triangular-gaussian membership function is denoted by using the normal and exponential data sets.
Esmaeil Shirazi,
Volume 14, Issue 1 (8-2020)
Abstract
In this paper, we consider an adaptive wavelet estimation for quantile density function based on block thresholding method and obtain it's convergence rate under L2 loss function over Besove function spaces. This work is an extension of results in Chesneau et. al. (2016) and shows that the block threshold estimator gets better convergence rate (Optimal) than the estimators proposed by Chesneau et. al. (2016). The performance of the proposed estimator is investigated with a simulation study.
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.
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.
Mehdi Balui, Einolah Deiri, Farshin Hormozinejad, Ezzatallah Baloui Jamkhaneh,
Volume 15, Issue 2 (3-2022)
Abstract
In most practical cases, to increase parameter estimation accuracy, we need an estimator with the least risk. In this, contraction estimators play a critical role. Our main purpose is to evaluate the efficiency of some shrinkage estimators of the shape parameter of the Pareto-Rayleigh distribution under two classes of shrinkage estimators. In this research, the purpose estimators' efficiency will be compared with the unbiased estimator obtained under the quadratic loss function. The relationship between these two classes of shrinkage estimators was examined, and then the relative efficiency of the proposed estimators was discussed and concluded via doing a Monte Carlo simulation.
Anis Iranmanesh, Farzaneh Oliazadeh, Vahid Fakoor,
Volume 15, Issue 2 (3-2022)
Abstract
In this article, we propose two non-parametric estimators for the past entropy based on length-biased data, and the strong consistency of the proposed estimators is proved. In addition, some simulations are conducted to evaluate the performance of the proposed estimators. Based on the results, we show that they have better performance in a different region of the probability distribution for length-biased random variables.
Shaho Zarei,
Volume 15, Issue 2 (3-2022)
Abstract
The most widely used model in small area estimation is the area level or the Fay-Herriot model. In this model, it is typically assumed that both the area level random effects (model errors) and the sampling errors have a Gaussian distribution. However, considerable variations in error components (model errors and sampling errors) can cause poor performance in small area estimation. In this paper, to overcome this problem, the symmetric α-stable distribution is used to deal with outliers in the error components. The model parameters are estimated with the empirical Bayes method. The performance of the proposed model is investigated in different simulation scenarios and compared with the existing classic and robust empirical Bayes methods. The proposed model can improve estimation results, in particular when both error components are normal or have heavy-tailed distribution.
Masumeh Ghahramani, Maryam Sharafi, Reza Hashemi,
Volume 16, Issue 1 (9-2022)
Abstract
One of the most critical challenges in progressively Type-II censored data is determining the removal plan. It can be fixed or random so that is chosen according to a discrete probability distribution. Firstly, this paper introduces two discrete joint distributions for random removals, where the lifetimes follow the two-parameter Weibull distribution. The proposed scenarios are based on the normalized spacings of exponential progressively Type-II censored order statistics. The expected total test time has been obtained under the proposed approaches. The parameters estimation are derived using different estimation procedures as the maximum likelihood, maximum product spacing and least-squares methods. Next, the proposed random removal schemes are compared to the discrete uniform, the binomial, and fixed removal schemes via a Monte Carlo simulation study in terms of their biases; root means squared errors of estimators and their expected experiment times. The expected experiment time ratio is also discussed under progressive Type-II censoring to the complete sampling plan.
Mr. Ali Rostami, Dr. Mohammad Khanjari Sadegh, Dr. Mohammad Khorashadizadeh,
Volume 16, Issue 2 (3-2023)
Abstract
In this article, we consider the estimation of R{r,k}= P(X{r:n1} < Y{k:n2}), when the stress X and strength Y are two independent random variables from inverse Exponential distributions with unknown different scale parameters. R{r,k} is estimated using the maximum likelihood estimation method, and also, the asymptotic confidence interval is obtained. Simulation studies and the performance of this model for two real data sets are presented.
Ali Rostami, Mohammad Khanjari Sadegh, Mohammad Khorashadizadeh,
Volume 17, Issue 1 (9-2023)
Abstract
This article considers the stress-strength reliability of a coherent system in the state of stress at the component level. The coherent series, parallel and radar systems are investigated. For 2-component series or parallel systems and radar systems, this reliability based on Exponential distribution is estimated by maximum likelihood, uniformly minimum variance unbiased and Bayes methods. Also, simulation studies have been done to check estimators' performance, and real data are analyzed.
Doctor Masoumeh Akbari, Mrs Arefeh Kasiri, Doctor Kambiz Ahmadi,
Volume 17, Issue 1 (9-2023)
Abstract
In this paper, quantile-based dynamic cumulative residual and failure extropy measures are introduced. For a presentation of their applications, first, by using the simulation technique, a suitable estimator is selected to estimate these measures from among different estimators. Then, based on the equality of two extropy measures in terms of order statistics, symmetric continuous distributions are characterized. In this regard, a measure of deviation from symmetry is introduced and how it is applied is expressed in a real example. Also, among the common continuous distributions, the generalized Pareto distribution and as a result the exponential distribution are characterized, and based on the obtained results, the exponentiality criterion of a distribution is proposed.
Fateme Sadat Mirsadooghi, Akram Kohansal,
Volume 17, Issue 2 (2-2024)
Abstract
In this paper, under adaptive hybrid progressive censoring samples, Bayes estimation of the multi-component reliability, with the non-identical-component strengths, in unit generalized Gompertz distribution is considered. This problem is solved in three cases. In the first case, strengths and stress variables are assumed to have unknown, uncommon parameters. In the second case, it is assumed that strengths and stress variables have two common and one uncommon parameter, so all of these parameters are unknown. In the third case, it is assumed that strengths and stress variables have two known common parameters and one unknown uncommon parameter. In each of these cases, Bayes estimation of the multi-component reliability, with the non-identical-component strengths, is obtained with different methods. Finally, different estimations are compared using the Monte Carlo simulation, and the results are implemented on one real data set.
Om-Aulbanin Bashiri Goudarzi, Abdolreza Sayyareh, Sedigheh Zamani Mehreyan,
Volume 19, Issue 1 (9-2025)
Abstract
The boosting algorithm is a hybrid algorithm to reduce variance, a family of machine learning algorithms in supervised learning. This algorithm is a method to transform weak learning systems into strong systems based on the combination of different results. In this paper, mixture models with random effects are considered for small areas, where the errors follow the AR-GARCH model. To select the variable, machine learning algorithms, such as boosting algorithms, have been proposed. Using simulated and tax liability data, the boosting algorithm's performance is studied and compared with classical variable selection methods, such as the step-by-step method.
Arezu Rahmanpour, Yadollah Waghei, Gholam Reza Mohtashami Borzadaran,
Volume 19, Issue 1 (9-2025)
Abstract
Change point detection is one of the most challenging statistical problems because the number and position of these points are unknown. In this article, we will first introduce the concept of change point and then obtain the parameter estimation of the first-order autoregressive model AR(1); in order to investigate the precision of estimated parameters, we have done a simulation study. The precision and consistency of parameters were evaluated using MSE. The simulation study shows that parameter estimation is consistent. In the sense that as the sample size increases, the MSE of different parameters converges to zero. Next, the AR(1) model with the change point was fitted to Iran's annual inflation rate data (from 1944 to 2022), and the inflation rate in 2023 and 2024 was predicted using it.
Hossein Haghbin,
Volume 19, Issue 2 (4-2025)
Abstract
In this paper, a novel approach for forecasting a time sequence of probability density functions is introduced, which is based on Functional Singular Spectrum Analysis (FSSA). This approach is designed to analyze functional time series and address the constraints in predicting density functions, such as non-negativity and unit integral properties. First, appropriate transformations are introduced to convert the time series of density functions into a functional time series. Then, FSSA is applied to forecast the new functional time series, and finally, the predicted functions are transformed back into the space of density functions using the inverse transformation. The proposed method is evaluated using real-world data, including the density of satellite imagery.
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