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.

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.  

SPI is based on fitting a gamma distribution to precipitation amounts in selected periods. Based on current research, the gamma distribution may not be fitted to annual precipitation of some regions. In order to evaluate this subject, annual precipitation have been used during 1958- 2007 at 11 Synoptic Stations in Iran. In first step, values of SPI and frequency of different classes of drought severity were calculated. The Kolmogorov–Smirnov test is used to assess the goodness of fitting most appropriate distribution function to annual precipitation. Then, according to equi-Probability transformation the values of SPI were modified. The impact of applying most appropriate distribution function was evaluated to change the frequency of different classes of drought severity in Modified Standardized Precipitation Index (MSPI). The results showed that annual precipitation in all stations do not fallow Gamma distribution as appropriate distribution function except for Rasht station. Using appropriate distribution function in a MSPI leads to changing the frequency and/or displacement of different classes in SPI. So displacements occurred in all classes of drought severity at Tehran and Gorgan synoptic stations. The Gorgan station with 15 events has the most changes in frequency classes.

Probability density functions of the involved random variables are essential for the reliability-based design of offshore structures. The objective of present research was the derivation of Probability density function (PDF) for the local joint flexibility (LJF) factor, fLJF, in two-planar tubular DK-joints commonly found in jacket-type offshore structures. A total of 162 finite element (FE) analyses were carried out on 81 FE models of DK-joints subjected to two types of axial loading. Generated FE models were validated using available experimental data, FE results, and design formulas. Based on the results of parametric FE study, a sample database was prepared for the fLJF values and density histograms were generated for respective samples based on the Freedman-Diaconis rule. Nine theoretical PDFs were fitted to the developed histograms and the maximum likelihood (ML) method was applied to evaluate the parameters of fitted PDFs. In each case, the Kolmogorov-Smirnov and chi-squared tests were used to evaluate the goodness of fit. Finally, the Inverse Gaussian model was proposed as the governing Probability distribution function for the fLJF. After substituting the values of estimated parameters, two fully defined PDFs were presented for the fLJF in tubular DK-joints subjected to two types of axial loading.

In this research for choosing the best distribution function for the annual maximum discharge (AMD) in the southern provinces of Iran; The daily discharge of 108 hydrometric stations (1983-2012) were used; Data were fitted with 65 Probability distribution functions. After the goodness of fit tests using the statistical calculations, the best distributions function for the AMD was determined and eventually the discharge amounts were calculated with different return periods and compared with the result of the common distribution functions like log-Pearson (III), log-normalIII and Weakby. The result shown, the Waekby distribution functions with the 2. 43% and the first rank, the log-PearsonIII with the frequency of 6. 13% and the second rank and log-normal III with the frequency of the 5. 6% and the third rand, gained the best statistical distribution. The MBE in AMD estimation showed that in 2. 5 and 10-year return period, the Weakby statistical distribution and in the 25. 5 and 100-year return period. The log-Pearson III statistical distribution has a better estimation. Comparing the RMSE with MAPE in both Weakby and log PearsonIII statistical distribution, it is found that Weakby statistical distribution has a better estimation in the different return periods in this index.

Agricultural sector is most dependent on climate, and climate is the main determinant of time, location, production resources, and productivity of agricultural activities. The first event of zero-degree temperature in fall and its last event in spring is important for agriculture. This information is used to determine the species suitable for planting in each area. The present study seeks to identify the Probability distribution function for extracting statistical characteristics of frost events in Iran. For this purpose, the history of early autumn and late spring frosts were extracted using daily minimum temperatures of 44 synoptic stations in Iran for a period of 30 years (1981-2010). After fitting various distributions, the best distribution was selected using Anderson-Darling goodness of fit test. Results indicated that most stations follow the Wakeby distribution. Based on the calculations, the first day of frost occurs in the highlands of the Northwest (Saqez, Hamedan, Ardabil, and Zanjan), Northeast (Bojnoord, Torbat-e Heydariyeh, Birjand, and also the Central Zagros Mountains (Shahr-e Kord), due to proximity with cold lands of the North such as Siberia and Northern Europe as well as early entry of westerly winds to this region compared to other regions of Iran will occur. And the latest event of the first day of frost occurs a little farther from the southern coast of Iran in a narrow strip along the coast and parts of the northern coasts (from Babolsar to Bandar Anzali). The earliest event of the last day of frost occurs in the same area in early February. The latest day of frost in Iran occurs in Azerbaijan, Kurdistan, Khorasan, and highlands of the province of Chahar Mahal and Bakhtiari

Membership function based on Probability density functionچندین روش به منظور برآورد تابع چگالی احتمال وجود دارد. از سوی دیگر، در نظریه مجموعه هایفازی یکی از روش های ساختن تابع عضویت بر پایه ی مجموعه داده، روش مبتنی بر تابع چگالی احتمال است.با توجه به روش های متداول در برآورد تابع چگالی، این مسئله می تواند به محاسبه انواع تابع عضویت بر پایهیک مجموعه داده منجر شود. در این مقاله، برخی از این روش ها بیان و با مثال عددی تشریح می شوند..

In this paper, the optical density distribution function obtained from the radiographic films at the voltages of 80-150 kV was investigated. Steel plates of 30×30 mm2 with thicknesses of 2 and 8 mm were irradiated according to the European standards with different currents at various times. The information of the radiographic films was converted into 8-bit numeric data by using a laser scanner with a resolution of 3200 dpi. The histograms obtained from these scans were compared with all applicable Probability functions. Due to the large number of the employed Probability functions, their compatibility was first assessed on the best and simplest histogram. Afterwards, the selected functions were used for the remaining films. In this way, the best Probability distribution function was determined. The same steps were taken for radiographic defects. Furthermore, the degree of adaptation of the Probability distribution functions applied to the base metal and the defects regions was also evaluated.

In this paper, we consider the determination methods of maximum entropy multivariate distributions with given prior under the constraints, that the marginal distributions or the marginals and covariance matrix are prescribed. Next, some numerical solutions are considered for the cases of unavailable closed form of solutions. Finally, these methods are illustrated via some numerical examples.