In this article new generalization of half-normal distribution as the half generalized normal distribution is introduced. ‎This distribution, contains the half-normal distribution as special case.‎ We provide mathematical properties of this distribution. We also derive the pdf, cdf, -th moment, the asymmetry and kurtosis coefficients and the moment generating function. We discuss some inferential aspects related to the maximum likelihood estimation. Finally we illustrate the flexibility of this type of distribution with applications to real data sets.

We consider the problem of inference about skewness parameter in skew-normal distribution and it's difficulties. An approximately maximum likelihood estimator that is based on some prior information is proposed. Finally the efficiency of proposed estimator is assessed both theoretically and by a simulation study.

In order to estimation genotypic correlation and heritability of some faba bean traits, 26 faba bean genotypes were evaluated in a randomized complete block design with three replications during 2014-16 growing seasons in Agricultural Research Sation of Borujerd located in Lorestan province, Iran. The restricted maximum likelihood (REML) was used to estimate the genotypic and phenotypic correlations, broad sence heritability and genetic gain. Analysis of variance based on least squares and REML indicated significant effect of genotype on days to maturity, plant height, hundred seed weight, pod length and dry seed yield. Genotype×year interactions were significant on all of the traits except of pod length. Borujerd cultivar (G26) and G20 had the highest dry seed yield in both of years. REML results indicated a significant positive genetic correlation between dry seed yield and biological yield and plant height. Also, there were a significant negative phenotypic correlation between dry seed yield and days to maturity, and significant positive phenotypic correlation between dry seed yield and plant height, biological yield and harvest index. So, the selection of early maturing genotypes with a higher yield is achievable and selection can be done to improve the performance of dry seed yield. Cluster analysis indicated variability among genotypes. According to values of broad sence heritability and genetic gain for plant height and high genetic correlation of this trait and dry seed yield; plant height can be used as a suitable trait for improving dry seed yield by selection.

Usually, we estimate the unknown parameter by observing a random sample and using the usual methods of estimation such as maximum likelihood method. In some situations, we have information about the real parameter in the form of a guess. In these cases, one may shrink the maximum likelihood or other estimators towards a guess value and construct a shrinkage estimator. In this paper, we study the behavior of a Bayes shrinkage estimator for the scale parameter of exponential distribution based on censored samples under an asymmetric and scale invariant loss function. To do this, we propose a Bayes shrinkage estimator and compute the relative efficiency between this estimator and the best linear estimator within a subclass with respect to sample size, hyperparameters of the prior distribution and the vicinity of the guess and real parameter. Also, the obtained results are extended to Weibull and Rayleigh lifetime distributions.

Gompertz-Poisson distribution is a three-parameter lifetime distribution with increasing, decreasing, increasing-decreasing and unimodal shape failure rate function and a composition of Gompertz and Poisson distributions cut at zero point that in this paper estimated the parameters of the distribution by maximum likelihood method and in order to confirm the calculated estimates, based on random sample with volumes of 100, 200, 300, 400 and 500 of Gompertz-Poisson distribution simulation study was conducted. Also with the help of two real data sets and comparing Gompertz-Poisson distribution with several other distributions of lifetime we show this distribution is a good model for data fitness related to lifetime.

BACKGROUND AND OBJECTIVES: Weibull distribution, introduced by a Swedish physicist named Weibull, is the most common model used in studies of reliability, longevity, quality control. It is widely used in various fields of science including insurance, medicine, and engineering . This distribution is flexible enough to model different data. The main goal of this research is to calculate insurance premiums and estimate Weibull distribution parameters using various estimation methods.METHODS: In this article, the parameters of Weibull distribution and net premium have been estimated using moment estimation, maximum likelihood, least squares of error, weighted least squares, percentage, Cramer-Von- Mises, mixture of moment and maximum-likelihood against outliers. R software was used for simulation and numerical calculations purposes and also Easyfit software was used to fit Weibull distribution to the real example data. In the end, two real data examples for obtaining various estimators of the premium in case of unknown parameters β and θ and known α are presented.FINDINGS: In this research bias, the mean square error of net premium and unknown parameters β and θ were obtained using different estimators for Weibull distribution data as well as the generalized variance of unknown parameters β and θ.CONCLUSION: In this part, the evaluation and comparison of the estimators using real and simulated data was done, which was obtained by different for real data. For example, in the moment method, was equal to 5, based on which the net premium is 3.37657. In the simulated data, according to k (number of outliers), n (sample size) and β and θ values, bias values, mean squared error and generalized variance of premium and different estimators were obtained. As an example, for n=10, k=1, β=1.5, θ=3 and α=70, by comparing the bias and generalized variance of the estimators, we come to the conclusion that based on the bias, the percentile estimator has a better performance than the other estimators. Simply put, it has less bias and according to the generalized variance, the maximum likelihood estimator has a better performance than other estimators and the estimators are consistent (the generalized variance decreases with the increase of the sample size). Based on the mean square error, the moment estimation has a better performance than other estimators.