Application of Univariate Probability Distributions Fitting With Monte Carlo Simulation

In this study, we present a univariate probability distribution through application of the three Sub and Super Exponential heavier-longer and lighter-shorter tails fitting. This univariate family includes the Lognormal, Gamma and Weibull distribution, the adequacy of the distribution tails is obtained by adequate Fitting Tests and descriptive Criterion. It emphasizes on tail values and is independent of the number of intervals. In this regards the time series analysis for the last three centuries of the logarithm population data sets over to Karachi region (from1729 to1946 and from 1951 to 2018) is used, which contains irregular and regular length and peaks, That peaks /tails fitting is attained by methods for validation and normality tests and defined by stochastic depiction. In other hand, Weibull and Lognormal distribution tails are found as heavier distribution by two validation tests (Maximum Likelihood Estimation and probability of correct selection), In the final section, the univariate probability distributions are used to Monte Carlo simulation for generating the actual population data, it indicates that the heavy-tailed Lognormal and Weibull distributions are also fitted contract than the more commonly seen lighter tailed Gamma distribution. So, the Monte Carlo Simulation performs the appropriate Lognormal and Weibull distributions for irregular and regular data and generate data values (298 and 69) from duration of 1729 to 2020 and 1951 to 2020. Copyright(c) The Author

International trade distributions and their relation with random fragmentation processes

A study of the distribution of the value of traded goods under the Harmonized System is presented. The ramifications of this classification system are found to exhibit an approximate power law decay, indicating complexity and self-organization in the nomenclature of traded merchandises. For almost all countries with available data, log-values of annually imported and exported goods are well described by three-parameter Weibull distributions. This distribution commonly appears in particles size distributions, suggesting a connection between random fragmentation processes and the mechanisms behind the international trade of merchandises. Analysis of the resulting values for the fitting parameters from 1995 to 2018 shows a nearly constant linear relationship between the parameters of the Weibull distributions, so that, for each country, the distribution of log-values can be approximately characterized by a single shape parameter [Formula: see text]. The empirical findings of this paper suggest that specialization on trading a constant set of goods prevents the values of all traded merchandises from growing/decreasing simultaneously.

A New Variable-Censoring Control Chart Using Lifetime Performance Index under Exponential and Weibull Distributions

In reliability theory or life testing, exponential distribution and Weibull distribution are frequently considered to model the lifetime of the components or systems. In this paper, we design a control chart based on the lifetime performance index using Type II censoring for exponential and Weibull distributions. Average run length helps to measure the performance of the proposed control chart. The optimal values of the number of failure items and decision criteria used to decide whether the process is in-control or out-of-control based on the sample results are determined such that the in-control average run length is as close as to the specified average run length values. We simulate the data to illustrate the performance of the proposed control chart.

A Probabilistic Model of the Unidirectional Tensile Strength of Fiber-Reinforced Polymers for Structural Design

In this paper, a statistical analysis of the tensile strength of FRP composites is conducted. A relatively large experimental database including 58 datasets is first constructed, and the Normal, Lognormal, and Weibull distributions are fitted to the data using a tail-sensitive Anderson–Darling statistic as the measure of goodness of fit. Fitting results show that the Normal, Lognormal, and Weibull distributions can be used to model the tensile strength of FRP composites. Then, the characteristic value for the tensile strength of FRP composites at a fixed percentile is analyzed. It is found that the Weibull distribution results in a higher safety margin in comparison to either the Normal or the Lognormal distribution. When the experimental justification, the theoretical justification, as well as the design conservativeness are taken into consideration, the Weibull distribution is the most recommended distribution to model the tensile strength of FRP composites. Furthermore, a probabilistic model considering the statistical uncertainty for the tensile strength for FRP composites is proposed. It is believed that the statistical uncertainty can be modeled as a reduction factor, and the recommended value of such factor for engineering design practices is provided based on regression analysis.

Robust Assessment on the Developments of Three Extended Exponential Models with Some New Properties and Applications

The extended exponential distribution introduced by Nadarajah and Haghighi in the year 2011, which is nowadays well known as NH distribution, has received increased attention in these days. In this paper, we provide a robust assessment report on the development of three more related extended versions of exponential (or Weibull) distributions. We assessed that which model was published earlier than the other ones and why the pioneer work was not cited properly or overlooked. For example, power generalized Weibull (PGW) introduced by Bagdonavic̆ios and Nikulin (and Nikulin and Haghighi) and extended Weibull by Dimitrakopoulou, Adamidis, and Loukas, which we call here as the DAL model, were published earlier than the NH model. The developments of these three models are stated. A new method for the construction of NH and DAL models is outlined. A literature review on NH and DAL models is presented, and generalized classes from these models are discussed. Furthermore, some corrections in NH moments are suggested, and alternative expressions for moments and incomplete moments of NH and DAL models are also developed.

Higher Order Moments of the Order Statistics for the Rectangular, Exponential, Gamma and Weibull Distributions

In this paper we discuss the problem of Higher Order Moments for the order Statistics for the Rectangular, Exponential, Gamma and Weibull distributions by finding the order statistic distributions for the base distribution and modified distributions, the base distribution is to deduce the corresponding distribution by the polynomial modifier. These higher order moments are very much useful in most of the Data sciences and Image analysis.