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Showing 13 results for Maximum Likelihood Estimation
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Volume 20, Issue 2 (10-2015)
Abstract
Methods for small area estimation have been received great attention in recent years due to growing demand for
reliable small area estimation that are needed in development planings, allocation of government funds and marking
business decisions. The key question in small area estimation is how to obtain reliable estimations when sample
size is small. When only a few observations(or even no observation) are available from a given small area, small
sample sizes lead to undesirably large standard errors. The only possible solution to the estimation problem is to
borrow strength from available data sets. This is accomplish by using appropriate linking models (included explicit
and implicit models) to increas the effect of sample size for estimation. The generalized linear mixed models and
the empirical best linear unbiased predictor, are extensively used to estimate reliable mean of small areas. In this
article,first we introduce the small area estimation.Then, to obtain reliable small area estimations we introduce the
Fay-Herriot model as a special case of the generalized linear mixed model. Finally, in an Simulation study we use
Iran 1382 agricultural census data to estimate orange production in Fars cities (small areas) in the year 1382 based
on Fay-Herriot model.
Dr farzad Eskandari, Ms imaneh Khodayari Samghabadi,
Volume 21, Issue 1 (9-2016)
Abstract
There are different types of classification methods for classifying the certain data. All the time the value of the variables is not certain and they may belong to the interval that is called uncertain data. In recent years, by assuming the distribution of the uncertain data is normal, there are several estimation for the mean and variance of this distribution. In this paper, we consider the mean and variance for each of the start and end of intervals. Thus we assume that the distribution of uncertain data is bivariate normal distribution. We used the maximum likelihood to estimate the means and variances of the bivariate normal distribution. Finally, Based on the Naive Bayesian classification, we propose a Bayesian mixture algorithm for classifying the certain and uncertain data. The experimental results show that the proposed algorithm has high accuracy.
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.
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.
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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.
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
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.
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.
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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