STATISTICAL analysis of fractional Brownian motion process is one of the most important issues in the field of stochastic processes. The most important issue in the study of this process is STATISTICAL INFERENCE about the Hurst parameters of the fractional Brownian motion. One of the methods for estimation of aforementioned parameter is maximum likelihood approach. Due to the computational complexity of this approach to give a closed estimate, it is attempting to derive the parameter estimated through the numerical method approach. Also, the theoretical result of the paper is evaluated in a simulation study for different scenarios.

Nonhomogeneous Poisson processes (NHPPs) are often used to model recurrent events, and there is thus a need to check model fit for such models. We study the problem of obtaining exact goodness-of-fit tests for certain parametric NHPPs, using a method based on Monte Carlo simulation conditional on sufficient statistics. A closely related way of obtaining exact confidence intervals in parametric models is also briefly considered.

With modern technology development, functional data analysis (FDA) has received considerable recent attention in many scientific fields. The estimation of mean in FDA is of interest, because it is not only important by itself but it is a prelude to other issues such as dimension reduction and modeling of functional data In this paper we construct a two-sample Behrens-Fisher problem when data are functions and obtain the asymptotic properties of the test statistic as data dimension increases with the sample size. The power of the proposed test is also investigated. The proposed test used for INFERENCE about the differences in the mean temperature functions of the Western and the South-western weather stations of Iran.

In this article, the hypothesis test and confidence interval for the fuzzy coefficients in the fuzzy weighted regression model with precise inputs and fuzzy outputs are discussed. By applying the weighted estimation method in estimating the coefficients and using the conventional fuzzy hypotheses in the fuzzy environment,, We are trying to determine the distribution of the available estimators, based on the bootstrap method so that we can decide to accept or reject the existing hypotheses. Therefore, at first, the required test statistics are calculated based on the bootstrap method. Then, by comparing the probability value and the given significance level, as in the classical method, the null hypothesis is accepted or rejected. Also, from another point of view, hypothesis testing based on bootstrap confidence intervals is also discussed. At the end, by analyzing a practical example with real data in housing, the approach investigated in hypothesis testing and confidence interval for the coefficients of the fuzzy regression model has been analyzed.

In this paper a new method of estimation, named Adjusted Probability Weighted Moment (APWM), is introduced which is an extension of the Probability Weighted Moment (PWM). Based on APWM, a STATISTICAL INFERENCE is carried out on the parameter of Uniform distribution on (0, q). The results are compared with the ones of the other methods like the Maximum Likelihood (ML) and PWM. The APWM outperforms the PWM and gives the results at least similar to ML.

Lifetime performance index is widely used as process capability index to evaluate the performance and potential of a process. In manufacturing industries, the lifetime of a product is considered to be conforming if it exceeds a given lower threshold value, so nonconforming products are those that fail to exceed this value. Nonconformities are so important that affect the safe or effective use of the products. This article deals with the processes that the products' lifetime is related to a two-component system, distributed as Farlie-Gumbel-Morgenstern (FGM) copula-based bivariate exponential and presen ts the probability of non-conforming products. Also, bootstrap upper confidence bounds are constructed and their performance are investigated in simulation study. In addition, Monte Carlo scheme is applied to do hypothesis testing on it. Finally, two example sets are presented to demonstrate the application of the proposed index.