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Showing 8 results for Approximation

Kobra Gholizadeh, Mohsen Mohammadzadeh, Zahra Ghayyomi,
Volume 7, Issue 1 (9-2013)
Abstract

In Bayesian analysis of structured additive regression models which are a flexible class of statistical models, the posterior distributions are not available in a closed form, so Markov chain Monte Carlo algorithm due to complexity and large number of hyperparameters takes long time. Integrated nested Laplace approximation method can avoid the hard simulations using the Gaussian and Laplace approximations. In this paper, consideration of spatial correlation of the data in structured additive regression model and its estimation by the integrated nested Laplace approximation are studied. Then a crime data set in Tehran city are modeled and evaluated. Next, a simulation study is performed to compare the computational time and precision of the models provided by the integrated nested Laplace approximation and Markov chain Monte Carlo algorithm

Nasrin Moradi, Abdolreza Sayyareh, Hanieh Panahi,
Volume 8, Issue 1 (9-2014)
Abstract

In this article, the parameters of the Exponentiated Burr type III distribution have been estimated based on type II censored data using maximum likelihood method with EM algorithm and Bayesian approach under Gamma prior distributions against the squared error, linex and entropy loss functions. Importance sampling technique and Lindley's approximation method have been applied to evaluate these Bayes estimates. The results are checked by simulation study and analyzing real data of acute myelogeneous disease. The Bayes estimates are, generally, better than the MLEs and all estimates improve by increasing sample size.

Fatemeh Hosseini, Elham Homayonfal,
Volume 10, Issue 2 (2-2017)
Abstract

Hierarchical spatio-temporal models are used for modeling space-time responses and temporally and spatially correlations of the data is considered via Gaussian latent random field with Matérn covariance function. The most important interest in these models is estimation of the model parameters and the latent variables, and is predict of the response variables at new locations and times. In this paper, to analyze these models, the Bayesian approach is presented. Because of the complexity of the posterior distributions and the full conditional distributions of these models and the use of Monte Carlo samples in a Bayesian analysis, the computation time is too long. For solving this problem, Gaussian latent random field with Matern covariance function are represented as a Gaussian Markov Random Field (GMRF) through the Stochastic Partial Differential Equations (SPDE) approach. Approximatin Baysian method and Integrated Nested Laplace Approximation (INLA) are used to obtain an approximation of the posterior distributions and to inference about the model. Finally, the presented methods are applied to a case study on rainfall data observed in the weather stations of Semnan in 2013.


Shahram Mansouri,
Volume 10, Issue 2 (2-2017)
Abstract

Among all statistical distributions, standard normal distribution has been the most important and practical distribution in which calculation of area under probability density function and cumulative distribution function are required. Unfortunately, the cumulative distribution function of this is, in general, expressed as a definite integral with no closed form or analytical solution. Consequently, it has to be approximated. In this paper, attempts have been made for Winitzki's approximation to be proved by a new approach. Then, the approximation is improved with some modifications and shown that the maximum error resulted from this is less than 0.0000584. Finally, an inverse function for computation of normal distribution quantiles has been derived.


Abouzar Bazyari,
Volume 11, Issue 1 (9-2017)
Abstract

The collective risk model of insurance company with constant initial capital when process of claims number have the poisson distribution with constant rate is considered. For computing the infinite time ruin probability the stochastic processes and differential equations are used. Also a formula is obtained to compute the Lundberg approximation in finding the approximate of infinite time ruin probability based on the distribution function of claims number. The numerical examples to illustrate these results are given and showed that for any value of initial capital the approximate of our infinite time ruin probability is closer to its real value rather than the ruin probability computed by other authors and has less error.


Akram Kohansal, Nafiseh Alemohammad, Fatemeh Azizzadeh,
Volume 14, Issue 2 (2-2021)
Abstract

The Bayesian estimation of the stress-strength parameter in Lomax distribution under the progressive hybrid censored sample is considered in three cases. First, assuming the stress and strength are two random variables with a common scale and different shape parameters. The Bayesian estimations of these parameters are approximated by Lindley method and the Gibbs algorithm. Second, assuming the scale parameter is known, the exact Bayes estimation of the stress-strength parameter is obtained. Third, assuming all parameters are unknown, the Bayesian estimation of the stress-strength parameter is derived via the Gibbs algorithm. Also, the maximum likelihood estimations are calculated, and the usefulness of the Bayesian estimations is confirmed, in comparison with them. Finally, the different methods are evaluated utilizing the Monte Carlo simulation and one real data set is analyzed.

Ali Mohammadian Mosammam, , Jorge Mateu,
Volume 16, Issue 2 (3-2023)
Abstract

An important issue in many cities is related to crime events, and spatio–temporal Bayesian approach leads to identifying crime patterns and hotspots. In Bayesian analysis of spatio–temporal crime data, there is no closed form for posterior distribution because of its non-Gaussian distribution and existence of latent variables. In this case, we face different challenges such as high dimensional parameters, extensive simulation and time-consuming computation in applying MCMC methods. In this paper, we use INLA to analyze crime data in Colombia. The advantages of this method can be the estimation of criminal events at a specific time and location and exploring unusual patterns in places.


Dr Adeleh Fallah,
Volume 19, Issue 1 (9-2025)
Abstract

In this paper, estimation for the modified Lindley distribution parameter is studied based on progressive Type II censored data. Maximum likelihood estimation, Pivotal estimation, and Bayesian estimation were calculated using the Lindley approximation and Markov chain Monte Carlo methods. Asymptotic, Pivotal, bootstrap, and Bayesian confidence intervals are provided. A Monte Carlo simulation study has been conducted to evaluate and compare the performance of different estimation methods. To further illustrate the introduced estimation methods, two real examples are provided.

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مجله علوم آماری – نشریه علمی پژوهشی انجمن آمار ایران Journal of Statistical Sciences

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