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.

The paper represents a physical blasting model in laboratory scale along with a photoGRAPHIC approach to describe the DISTRIBUTION of blasted rock materials. For this purpose, based on we bull PROBABILITY DISTRIBUTION FUNCTION, eight samples each weighted 100 kg, were obtained. Four pictures from four different section of each sample were taken. Then, pictures were converted into GRAPHIC FILES with characterizing boundary of each piece of rocks in the samples. Error caused due to perspective were eliminated. Volume of each piece of the blasted rock materials and hence the required sieve size, each piece of rock to pass through, were calculated. Finally, original blasted rock size DISTRIBUTION was compared with that obtained from the photoGRAPHIC method. The paper concludes with presenting an approach to convert the results of photoGRAPHIC technique into size DISTRIBUTION obtained by seive analysis with sufficient verification.

In this paper, the maximum liklihood estimation, unbiased estimations with minimum variance, percentile estimation, best percentile estimation single-observation estimation and the best percentile estimation two-observations in class which are based on order statistics are calculated in two sections for PROBABILITY density and cumulative DISTRIBUTION FUNCTIONs of the beta WEIBULL geometric DISTRIBUTION, specially with bathtub-shaped and unimodal failure rate which are useful for modeling of data related to reliability and lifetime. Furthermore, through the simulation method of Monte Carlo and calculation of average square of errors of estimators, they are subjected to comparisons ultimately, the desirable estimator in each section is determined.

New and renewable energies are of basic elements for the development of countries. Therefore,estimation of these energy sourcesseems indispensible.In this article,usingthree - hour data of the direction and speed of wind, wind energy potential in Ardebil province synoptic stations is examined. Based on this research, wind energy density in Ardebil, Khalkhal, Pars-Abad and Meshkinshahr synoptic stations are 362.55, 56.35, 60.24, 375.06 W/m2 respectively. Experimental PROBABILITY of data using WEIBULL DISTRIBUTION was calculated and according to chi-square test, this FUNCTION is a suitable one to fit with wind data. Having an eye on the time during which the speed of wind is above 4 m/s in this study, Ardebil synoptic station can be considered as a suitable area for using the wind energy.

The products of GRAPHIC design applications, leave behind traces of digital information which can be used during a digital forensic investigation in cases where counterfeit documents have been created. This paper analyzes the digital forensics involved in the creation of counterfeit documents. This is achieved by first recognizing the digital forensic artifacts left behind from the use of GRAPHIC design applications, and then analyzing the FILES associated with these applications. When analyzing digital forensic artifacts generated by an application, the specific focus is on determining whether the GRAPHIC design application was installed, whether the application was used, and determining whether an association can be made between the application’s actions and such a digital crime. This is accomplished by locating such information from the registry, log FILES and prefetch FILES. The file analysis involves analyzing FILES associated with these applications for file signatures and metadata. In the end it becomes possible to determine if a system has been used for creating counterfeit documents or not.

Since the inverse WEIBULL DISTRIBUTION is one of the well-known lifetime DISTRIBUTIONs in statistical inference‎, ‎estimating its parameters‎, ‎as well as estimating its PROBABILITY density FUNCTION and cumulative DISTRIBUTION FUNCTION through various statistical methods‎, ‎is recommended‎. ‎Throughout this study‎, ‎we develop the best two-observation percentile estimation for both the PROBABILITY density FUNCTION and cumulative DISTRIBUTION FUNCTION associated with the inverse WEIBULL DISTRIBUTION‎. ‎To gauge its efficacy‎, ‎we conduct a comparative analysis‎, ‎pitting the best two-observation percentile estimation against estimations derived through maximum likelihood and percentiles‎, ‎utilizing Monte Carlo simulations and scrutiny of two real datasets.

In this paper we focus on two topics. Firstly, we propose $U$-statistics for the WEIBULL DISTRIBUTION parameters. The consistency and asymptotically normality of the introduced $U$-statistics are proved theoretically and by simulations. Several of methods have been proposed for estimating the parameters of WEIBULL DISTRIBUTION in the literature. These methods include: the generalized least square type 1, the generalized least square type 2, the $L$-moments, the Logarithmic moments, the maximum likelihood estimation, the method of moments, the percentile method, the weighted least square, and weighted maximum likelihood estimation. Secondly, due to lack of a comprehensive comparison between the WEIBULL DISTRIBUTION parameters estimators, a comprehensive comparison study is made between our proposed $U$-statistics and above nine estimators. In our knowledge, this work is the most comprehensive comparison study for the estimators for the WEIBULL DISTRIBUTION. Based on simulations, it turns out that different estimators may appeal for different range of the parameters. So, practitioners are allowed to chose the best estimator that is suggested by the goodness-of-fit criteria.

Accurate estimation of delay is difficult because of the randomness of traffic flow and large number of factors affecting intersection capacity. Existing delay models provide only approximated point of estimates of signalized intersections. Identification and evaluation of PROBABILITY DISTRIBUTION of delay can be beneficial in understanding the nature of its variability at signalized intersections. In this study travel time delay data at three per-timed signalized intersections in Tehran, Iran were evaluated. The main purpose of this research is to present a delay DISTRIBUTION prediction model based on the data collected at some signalized intersections in Tehran. For this purpose the following steps have been taken:1. Literature reviews on queuing theory and existing delay models, well as well as theoretical support for the study.2. Sampling and data collection regarding delay of vehicles in some fixed time signalized intersections in Tehran.3. Determination of delay DISTRIBUTION FUNCTIONs by existing vehicles delays values obtained from the data. For this purpose the frequency of delays (data) in various intervals was calculated and then, based on the obtained histogram of the data, a few DISTRIBUTION FUNCTIONs (i.e. WEIBULL, Gamma, Beta, Normal, Erlong, Triangular, Exponential and Uniform) were fitted to this data and consequently the best delay DISTRIBUTION FUNCTION was obtained.4. Presentation of a model for predicting the delay time in some signalized intersections in Tehran.Hence, delay PROBABILITY DISTRIBUTION FUNCTIONs were developed for each signalized intersection using Arena simulation software. Results of simulation show that WEIBULL DISTRIBUTION FUNCTION provided better fits for delay data at all three intersections. The two parameters of this DISTRIBUTION were estimated by "average delay" and "g/c" ratio.