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Showing 25 results for Estimation
Fattaneh Nezampoor, Alireza Soleimani,
Volume 22, Issue 1 (12-2017)
Abstract
In this paper some properties of logistics - x family are discussed and a member of the family, the logistic–normal distribution, is studied in detail. Average deviations, risk function and fashion for logistic–normal distribution is obtained. The method of maximum likelihood estimation is proposed for estimating the parameters of the logistic–normal distribution and a data set is used to show applications of logistic–normal distribution.
Miss Elaheh Kadkhoda, Mr Morteza Mohammadi, Dr Gholam Reza Mohtashami Borzadaran,
Volume 22, Issue 1 (12-2017)
Abstract
Generalized Lambda Distribution is an extension of Tukey's lambda distribution, that is very flexible in modeling information and statistical data. In this paper, We introduced two parameterization of this distribution. Then We estimate parameters by moment matching, percentile, starship and maximum likelihood methods and compare two parameterization and parameter estimation methods with Kolmogorov-Smirnov test.
Ali Hedayati, Esmaile Khorram, Saeid Rezakhah,
Volume 22, Issue 2 (3-2018)
Abstract
Maximum likelihood estimation of multivariate distributions needs solving a optimization problem with large dimentions (to the number of unknown parameters) but two- stage estimation divides this problem to several simple optimizations. It saves significant amount of computational time. Two methods are investigated for estimation consistency check. We revisit Sankaran and Nair's bivariate Pareto distribution as an example. Two data sets (simulated data and real data) have been analyzed for illustrative purposes.
Anita Abdollahi Nanvapisheh,
Volume 22, Issue 2 (3-2018)
Abstract
In this paper, first, we investigate probability density function and the failure rate function of some families of exponential distributions. Then we present their features such as expectation, variance, moments and maximum likelihood estimation and we identify the most flexible distributions according to the figure of probability density function and the failure rate function and finally we offer practical examples of them.
Ali Shadrokh, Shahrastani Shahram Yaghoobzadeh,
Volume 22, Issue 2 (3-2018)
Abstract
In this paper, a new five-parameter so-called Beta-Gompertz Geometric (BGG) distribution is introduced that can have a decreasing, increasing, and bathtub-shaped failure rate function depending on its parameters. Some mathematical properties of the this distribution, such as the density and hazard rate functions, moments, moment generating function, R and Shannon entropy, Bonferroni and Lorenz curves and the mean deavations are provided. We discuss maximum likelihood estimation of the BGG parameters from one observed sample. At the end, in order to show the BGG distribution flexibility, an application using a real data set is presented.
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Volume 22, Issue 2 (3-2018)
Abstract
In this paper, a new probability distribution, based on the family of hyperbolic cosine distributions is proposed and its various statistical and reliability characteristics are investigated. The new category of HCF distributions is obtained by combining a baseline F distribution with the hyperbolic cosine function. Based on the base log-logistics distribution, we introduce a new distribution so-called HCLL and derive the various properties of the proposed distribution including the moments, quantiles, moment generating function, failure rate function, mean residual lifetime, order statistics and stress-strength parameter. Estimation of the parameters of HCLL for a real data set is investigated by using three methods: maximum likelihood, Bayesian and bootstrap (parametric and non-parametric). We evaluate the efficiency of the maximum likelihood estimation method by Monte Carlo simulation.
In addition, in the application section, by using a realistic data set, the superiority of HCLL model to generalized exponential, Weibull, hyperbolic cosine exponential, gamma, weighted exponential distributions is shown through the different criteria of selection model.
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Volume 23, Issue 1 (9-2018)
Abstract
In this paper some properties of Beta - X family are discussed and a member of the family,the beta– normal distribution, is studied in detail.One real data set are used to illustrate the applications of the beta-normal distribution and compare that to gamma - normal and Birnbaum-Saunders distriboutions.
Dr. Mehdi Shams,
Volume 23, Issue 2 (3-2019)
Abstract
In this paper, after introducing exponential family and a history of work done by researchers in the field of statistics, some applications of this family in statistical inference especially in estimation problem,statistical hypothesis testing and statistical information theory concepts will be discussed.
Ali Shadrokh, Shahrastani Shahram Yaghoobzadeh,
Volume 24, Issue 1 (9-2019)
Abstract
In this study, E-Bayesian and hierarchical Bayesian of parameter of Rayleigh distribution under progressive type-II censoring sampales and the efficiency of the proposed methods has been compared with each and Bayesian estimator using Monte Carlo simulation.
Dr. Mehdi Shams, Dr. Gholamreza Hesamian,
Volume 24, Issue 1 (9-2019)
Abstract
In this paper after introduce Ito integral we discuss filtering problem. In filtering problem there are two stochastic differential equations (system and observation) that given the observations we must find the best estimate for the random process of the system based on these observations. At last we give some useful examples.
Shahrastani Shahram Yaghoobzadeh,
Volume 24, Issue 1 (9-2019)
Abstract
In this paper, reliability in multi-component stress-strength models, when the stress and strength variables are inverse Rayleigh distributions with different parameters of alpha and beta. Estimates of the maximum likelihood, Bayesian and empirical Bayesian are estimated. Then, with the help of Monte Carlo simulation and two real data sets, these estimation methods are compared.
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Volume 24, Issue 2 (3-2020)
Abstract
The minimum density power divergence method provides a robust estimate in the face of a situation where the dataset includes a number of outlier data.
In this study, we introduce and use a robust minimum density power divergence estimator to estimate the parameters of the linear regression model and then with some numerical examples of linear regression model, we show the robustness of this estimator in the face of a dataset which includes a number of outliers.
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Volume 24, Issue 2 (3-2020)
Abstract
In the analysis of Bernoulli's variables, an investigation of the their dependence is of the prime importance. In this paper, the distribution of the Markov logarithmic series is introduced by the execution of the first-order dependence among Bernoulli variables. In order to estimate the parameters of this distribution, maximum likelihood, moment, Bayesian and also a new method which called the expected Bayesian method (E-Bayesian) are employed. In continuation, using a simulation study, it is shown that the expected Bayesian estimator out performed over the other estimators.
Fatemeh Hossini, Omid Karimi,
Volume 25, Issue 1 (1-2021)
Abstract
In spatial generalized linear mixed models, spatial correlation is assumed by adding normal latent variables to the model. In these models because of the non-Gaussian spatial response and the presence of latent variables, the likelihood function cannot usually be given in a closed form, thus the maximum likelihood approach is very challenging. The main purpose of this paper is to introduce two new algorithms for the maximum likelihood estimations of parameters and to compare them in terms of speed and accuracy with existing algorithms. The presented algorithms are applied to a simulation study and their performances are compared.
Dr. Shahram Yaghoobzadeh Shahrestani, Dr. Reza Zarei,
Volume 25, Issue 1 (1-2021)
Abstract
Whenever approximate and initial information about the unknown parameter of a distribution is available, the shrinkage estimation method can be used to estimate it. In this paper, first, the E-Bayesian estimation of the parameter of an inverse Rayleigh distribution under the general entropy loss function is obtained. Then, the shrinkage estimate of the inverse Rayleigh distribution parameter is investigated using the guess value. Also, using Monte Carlo simulations and a real data set, the proposed shrinkage estimation is compared with the UMVU and E-Bayesian estimators based on the relative efficiency criterion.
Ehsan Bahrami Samani, Samira Bahramian,
Volume 26, Issue 1 (12-2021)
Abstract
The occurrence of lifetime data is a problem which is commonly encountered in various researches, including surveys, clinical trials and epidemioligical studies. Recently there has been extensive methodological resarech on analyzing lifetime data. Howerver, because usually little information from data is available to corretly estimate, the inferences might be sensitive to untestable assumptions which this calls for a sensitivity analysis to be performed.
In this paper, we describe how to evaluate the effect that perturbations to the Log-Beta Weibull Regression Responses. Also, we review and extend the application and interpretation of influence analysis methods using censored data analysis. A full likelihood-based approach that allows yielding maximum likelihood estimates of the model parameters is used. Some simulation studies are conducted to evalute the performance of the proposed indices in ddetecting sensitivity of key model parameters. We illustrate the methods expressed by analyzing the cancer data.
Dr. Abouzar Bazyari,
Volume 26, Issue 2 (3-2022)
Abstract
In this paper, a generalization of the Gumbel distribution as the cubic transmuted Gumbel distribution based on the cubic ranking transmutation map is introduced. It is shown that for some of the parameters, the proposed density function is mesokurtic and for others parameters the density function is platykurtic function. The statistical properties of new distribution, consist of survival function, hazard function, moments and moment generating function have been studied. The parameters of cubic transmuted Gumbel distribution are estimated using the maximum likelihood method. Also, the application of the cubic transmuted Gumbel distribution is shown with two numerical examples and compared with Gumbel distribution and transmuted Gumbel distribution. Finally, it is shown that for a data set, the proposed cubic transmuted Gumbel distribution is better than Gumbel distribution and transmuted Gumbel distribution.
Ms. Zahra Jafarian Moorakani, Dr. Heydar Ali Mardani-Fard,
Volume 27, Issue 1 (3-2023)
Abstract
The ordinary linear regression model is $Y=Xbeta+varepsilon$ and the estimation of parameter $beta$ is: $hatbeta=(X'X)^{-1}X'Y$. However, when using this estimator in a practical way, certain problems may arise such as variable selection, collinearity, high dimensionality, dimension reduction, and measurement error, which makes it difficult to use the above estimator. In most of these cases, the main problem is the singularity of the matrix $X'X$. Many solutions have been proposed to solve them. In this article, while reviewing these problems, a set of common solutions as well as some special and advanced methods (which are less favored by someone, but still have the potential to solve these problems intelligently) to solve them.
Shahrastani Shahram Yaghoobzadeh Shahrastani, Amrollah Jafari,
Volume 28, Issue 1 (9-2023)
Abstract
In this article, queunig model $M/M/1$ is Considered, in which the innterarrival of customers have an exponenial disributon with the parameter $lambda$ and the service times have an exponenial disributon with the parameter $mu$ and are independent of the interarrival times. it is also assumed that the system is active until $T$. Then, under this stopping time Bayesian, $E$-Bayesian and hierarchical Bayesian estimations of the traffic intensity parameter of this queuing model are obtained under the general entropy loss function and considering the gamma and erlang prior distributions for parameters $lambda$ and $mu$, respicctively. Then, using numerical analysis and based on a new index, Bayesian, $E$-Bayesian and hierarchical Bayesian estimations are compared.
Dr Fatemeh Shahsanaei, Dr Rahim Chinipardaz,
Volume 28, Issue 2 (3-2024)
Abstract
Circular data are measured in angles or directions. In many cases of sampling, instead of a random sample, we deal with a weighted model. In such sampling, observations are provided throughout with a positive function, weight function. This article deals with weight distributions in circular data. According to von Mises distrinution is the most widely used distribution for modeling circular data, maximum likelihood estimation of parameters in weighted von Mises distributions is investigated. In a simulation study, different weights are compared in the Van Mises circular distribution.
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