Mathematical Researches

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In this Paper, We propose a new three-parameter lifetime of Power Series distributions of the Family Gampertz with decreasing, increasing, increasing-decreasing and unimodal Shape failure rate. The distribution is a Compound version of of the Gampertz and Zero-truncated Possion distributions, called the Gampertz-Possion distribution (GPD). The density function, the hazard rate function, a general expansion for moments, the density of the order statistic, and the maen and median deviations of the GPD are derived and studied in detail. The maximum likelihood estimation procedure is discussed and an algorithm EM is provided for estimating the parameters. The asymptotic confidence Intervals for the parameters are also obtained based on asymptotic variance covariance matrix.

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Thin plate and spherical splines are nonparametric methods suitable for spatial data analysis. Thin plate splines acquire efficient practical and high precision solutions in spatial interpolations. Two components in the model fitting is considered: spatial deviations of data and the model roughness. On the other hand, in parametric regression, the relationship between explanatory and response variables is considered as a functions based on minimizing sum of squares deviations criterion. In the current study, precision of the nonparametric methods that is thin plate spline and spherical spline is numerically compared with parametric multiple regression based on residual standard errors criterion by applying R software. Besides, precision of the fitted models is assessed for different sample sizes. Furthermore, the effect of different correlation coefficients is investigated by comparing precision of the fitted models for the three considered methods

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In this paper, we consider a three parametric regularly varying generalized Hypergeometric distribution which have been generated by Birth-Death process for describing phenomena in bioinformatics (Danielian and Astola, 2006). Under satisfying some conditions, we obtain the system of likelihood equations which its solution coincides with the maximum likelihood estimators. The given maximum likelihood estimators are the same as some moment estimators.
Moreover, an approximate computation of the maximum likelihood estimations for the unknown parameters is given. Using MCMC, simulation studies are proposed.
Finally, in order to present applications, some real data sets in bioinformatics are fitted with the model. Based on some important criterions, this model is compared with four other discrete distributions in bioinformatics. We see that the generalized Hypergeometric distribution provides a better fit than four other discrete distributions../files/site1/files/61/9(1).pdf
 

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In this paper, we consider the problem of two sided hypothesis testing for the parameter of coefficient of variation of an inverse Gaussian population. An approach used here is the modified signed log-likelihood ratio (MSLR) method which is the modification of traditional signed log-likelihood ratio test. Previous works show that this proposed method has third-order accuracy whereas the traditional approach has first-order one. Indeed, these methods are based on likelihood with a higher order of accuracy. For this reason, we are interested in using this method for inference about the parameter of coefficient of variation of an inverse Gaussian distribution. All necessary formulas for obtaining MSLR statistic are provided. Numerically, the performances of this method are compared with classical approaches, in terms of empirical type-I error rate and empirical test power. Simulation results show that the empirical type-I error rates of MSLR are close to nominal type-I error rate, even for small sample sizes whereas the traditional approaches are reliable only for large sample sizes. Comparing the empirical power sizes shows that the power of MSLR method is superior to other considered methods in some settings, by regarding that the competing approaches cannot perform well in controlling the type-I error probability because their empirical type-I error rates are far from the nominal type-I error rate. Finally, we illustrate the proposed methods using a real data set and then we conclude the paper.

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In this paper, the two-observational  percentile, percentile and maximum likelihood estimation of the probability density function of  Inverse Weibull random variable are studied. Finally, these estimates are compared using simulation studies and a real data.

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In this paper, the probability density function of the process, its trend functions, the maximum likelihood estimate and the confidence interval of the parameters are calculated. This paper investigates a nonhomogeneous state of a diffusion process with a time-dependent velocity reduction coefficient. First, the process probability density function and trend functions are calculated and then, using discrete sampling, statistical inferences such as estimating the parameters by the maximum likelihood method, finding the distribution of the obtained estimators and the confidence interval of the parameters are performed. Finally, for the simulated data, the applications of this model are introduced.

In this paper, from the point of view of statistical inference, stochastic differential equation models are studied. A heterogeneous case of a diffusion process with time-dependent deceleration coefficient and stochastic differential equation models with random effects are investigated and an approximation for the nonlinear stochastic differential equation is presented. Also, with the help of time series analysis and statistical methods, the parameters of stochastic differential equation models are estimated.At the end, the application of invariant copulas in the modeling of stochastic differential equations is expressed. In each of these cases, the process probability density function and trend functions are calculated, and statistical inferences such as point estimation, interval estimation, selection of the best model, and numerical analyzes and simulations are performed in stochastic differential equations.