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Showing 25 results for Estimation
Mr Mousa Abdi, Dr Akbar Asgharzadeh,
Volume 18, Issue 2 (3-2014)
Abstract
For computing different point estimates such as method of moment and maximum like-lihood estimates and different interval estimates (classical confidence interval, unbi-ased confidence interval, HPD interval), we may deal with the equations which need be solved numerically. In this paper, some numerical methods for solving these type of equations are reviewed in S-PLUS package. Various examples are presented to illus-trate the methods described.
Mrs Zahra Niknam, Dr mohammad Hossein Alamatsaz,
Volume 20, Issue 1 (4-2015)
Abstract
In many issues of statistical modeling, the common assumption is that observations are normally distributed. In
many real data applications, however, the true distribution is deviated from the normal. Thus, the main concern of
most recent studies on analyzing data is to construct and the use of alternative distributions. In this regard, new
classes of distributions such as slash and skew-slash family of distributions have been introduced .This has been the
main concern of many researcher’s investigations in recent decades. Slash distribution, as a heavy tailed symmetric
distribution, is known in robust studies. But since , in empirical examples, there are many situations where symmetric
distributions are not suitable for fitting the data study of skew distributions has become of particular importance.In
this paper we introduce skew-slash distribution and study their properties. Finally, some applications to several real
data sets are illustrated in order to show the importance of the distribution in regression models.
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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.
Shahrastani Shahram Yaghoobzadeh,
Volume 21, Issue 2 (3-2017)
Abstract
In this study, E-Bayesian of parameters of two parameter exponential distribution under squared error loss function is obtained. The estimated and the efficiency of the proposed method has been compared with Bayesian estimator using Monte Carlo simulation.
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.
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