W-Peakedness: A Simulation based Study

2015 ◽  
Vol 1 (1) ◽  
Author(s):  
Suboohi Safdar ◽  
Dr. Ejaz Ahmed
Keyword(s):  
Probability Distributions ◽  
Extensive Study ◽  
Descriptive Statistics ◽  
Target Point ◽  
Density Functions ◽  
Central Value ◽  
Distribution Shape ◽  
Simulation Based ◽  
Different Shapes ◽  
Kurtosis Coefficient

Kurtosis is a commonly used descriptive statistics. Kurtosis “Coefficient of excess” is critically reviewed in different aspects and is called as, measuring the fatness of the tails of the density functions, concentration towards the central value, scattering away from the target point or degree of peakedness of probability distribution. Kurtosis is referred to the shape of the distribution but many distributions having same kurtosis value may have different shapes while Kurtosis may exist when peak of a distribution is not in existence. Through extensive study of kurtosis on several distributions, Wu (2002) introduced a new measure called “W-Peakedness” that offers a fine capture of distribution shape to provide an intuitive measure of peakedness of the distribution which is inversely proportional to the standard deviation of the distribution. In this paper the work is extended for different others continuous probability distributions. Empirical results through simulation illustrate the proposed method to evaluate kurtosis by W-peakedness

MODELLING A COST PROFILE FOR ROAD PROJECTS

2020 ◽  
Author(s):  
Opeoluwa Akinradewo ◽  
Clinton Aigbavboa ◽  
Ayodeji Emmanuel Oke ◽  
Harrison Coffie
Keyword(s):  
Probability Distributions ◽  
Descriptive Analysis ◽  
Construction Cost ◽  
Cost Data ◽  
Density Functions ◽  
Cost Overrun ◽  
Historical Cost ◽  
Road Projects ◽  
Pro Forma

One of the vital success elements of a construction project is the accuracy of the estimation of construction cost. This study is aimed at developing a cost profile for road projects in Ghana. Pro-forma was designed to retrieve historical cost data of completed road projects in Ghana. The pro-forma retrieved data such as the initial budgeted cost and final construction cost of road projects, location of road projects, features of road projects, the scope of road projects (New project, renovation work, upgrade work or replacement work), type of road projects and classification of road projects. Cost data were analysed using descriptive analysis and probability distributions such as Cumulative Density Functions and Probability Density Functions. From findings, estimates prepared for road projects in Ghana can be expected to be below the final construction cost by about 20% while most of the completed road projects in Ghana experience cost overrun.

A Computationally Efficient Evolutionary Algorithm for Real-Parameter Optimization

2002 ◽  
Vol 10 (4) ◽  
pp. 371-395 ◽  
Author(s):  
Kalyanmoy Deb ◽  
Ashish Anand ◽  
Dhiraj Joshi
Keyword(s):  
Parameter Optimization ◽  
Optimization Problems ◽  
Research Effort ◽  
Probability Distributions ◽  
Scale Up ◽  
Extensive Study ◽  
Evolution Strategy ◽  
Real Parameter ◽  
Test Problems ◽  
Main Research

Due to increasing interest in solving real-world optimization problems using evolutionary algorithms (EAs), researchers have recently developed a number of real-parameter genetic algorithms (GAs). In these studies, the main research effort is spent on developing an efficient recombination operator. Such recombination operators use probability distributions around the parent solutions to create an offspring. Some operators emphasize solutions at the center of mass of parents and some around the parents. In this paper, we propose a generic parent-centric recombination operator (PCX) and a steady-state, elite-preserving, scalable, and computationally fast population-alteration model (we call the G3 model). The performance of the G3 model with the PCX operator is investigated on three commonly used test problems and is compared with a number of evolutionary and classical optimization algorithms including other real-parameter GAs with the unimodal normal distribution crossover (UNDX) and the simplex crossover (SPX) operators, the correlated self-adaptive evolution strategy, the covariance matrix adaptation evolution strategy (CMA-ES), the differential evolution technique, and the quasi-Newton method. The proposed approach is found to consistently and reliably perform better than all other methods used in the study. A scale-up study with problem sizes up to 500 variables shows a polynomial computational complexity of the proposed approach. This extensive study clearly demonstrates the power of the proposed technique in tackling real-parameter optimization problems.

On the wind resource in Algeria: Probability distributions evaluation

2020 ◽  
pp. 095765092097588
Author(s):  
Houdayfa Ounis ◽  
Nawel Aries
Keyword(s):  
Wind Speed ◽  
Probability Distribution ◽  
Probability Distributions ◽  
Resource Assessment ◽  
Descriptive Statistics ◽  
The Other ◽  
Wind Speeds ◽  
Wind Resource Assessment ◽  
The Mean ◽  
Wind Resource

The present study aims to present a contribution to the wind resource assessment in Algeria using ERA-Interim reanalysis. Firstly, the ERA-Interim reanalysis 10 m wind speed data are considered for the elaboration of the mean annual 10 m wind speed map for a period starting from 01-01-2000 to 31-12-2017. Moreover, the present study intends to highlight the importance of the descriptive statistics other than the mean in wind resource assessment. On the other hand, this study aims also to select the proper probability distribution for the wind resource assessment in Algeria. Therefore, nine probability distributions were considered, namely: Weibull, Gamma, Inverse Gaussian, Log Normal, Gumbel, Generalized Extreme Value (GEV), Nakagami, Generalized Logistic and Pearson III. Furthermore, in combination with the distribution, three parameter estimation methods were considered, namely, Method of Moment, Maximum Likelihood Method and L-Moment Method. The study showed that Algeria has several wind behaviours due to the diversified topographic, geographic and climatic properties. Moreover, the annual mean 10 m wind speed map showed that the wind speed varies from 2.3 to 5.3 m/s, where 73% of the wind speeds are above 3 m/s. The map also showed that the Algerian Sahara is windiest region, while, the northern fringe envelopes the lowest wind speeds. In addition, it has been shown that the study of the mean wind speeds for the evaluation of the wind potential alone is not enough, and other descriptive statistics must be considered. On the other hand, among the nine considered distribution, it appears that the GEV is the most appropriate probability distribution. Whereas, the Weibull distribution showed its performance only in regions with high wind speeds, which, implies that this probability distribution should not be generalized in the study of the wind speed in Algeria.

A New Approach to Probability in Engineering Design and Optimization

1984 ◽  
Vol 106 (1) ◽  
pp. 5-10 ◽  
Author(s):  
J. N. Siddall
Keyword(s):  
Probability Density ◽  
Engineering Design ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Density Functions ◽  
New Approach ◽  
Design And Optimization ◽  
Evolutionary Technique ◽  
Probability And Statistics

The anomalous position of probability and statistics in both mathematics and engineering is discussed, showing that there is little consensus on concepts and methods. For application in engineering design, probability is defined as strictly subjective in nature. It is argued that the use of classical methods of statistics to generate probability density functions by estimating parameters for assumed theoretical distributions should be used with caution, and that the use of confidence limits is not really meaningful in a design context. Preferred methods are described, and a new evolutionary technique for developing probability distributions of new random variables is proposed. Although Bayesian methods are commonly considered to be subjective, it is argued that, in the engineering sense, they are really not. A general formulation of the probabilistic optimization problem is described, including the role of subjective probability density functions.

scholarly journals Characterizations of Some Probability Distributions with Completely Monotonic Density Functions

2021 ◽  
pp. 51-64
Author(s):  
Mohammad Shakil ◽  
Dr. Mohammad Ahsanullah ◽  
Dr. B. M. G. Kibria Kibria
Keyword(s):  
Probability Distribution ◽  
Probability Density ◽  
Probability Distributions ◽  
Random Variable ◽  
Record Values ◽  
Density Functions ◽  
Exponential Distributions ◽  
Completely Monotonic ◽  
Percentage Points ◽  
Generalized Gamma Function

For a non-negative continuous random variable , Chaudhry and Zubair (2002, p. 19) introduced a probability distribution with a completely monotonic probability density function based on the generalized gamma function, and called it the Macdonald probability function. In this paper, we establish various basic distributional properties of Chaudhry and Zubair’s Macdonald probability distribution. Since the percentage points of a given distribution are important for any statistical applications, we have also computed the percentage points for different values of the parameter involved. Based on these properties, we establish some new characterization results of Chaudhry and Zubair’s Macdonald probability distribution by the left and right truncated moments, order statistics and record values. Characterizations of certain other continuous probability distributions with completely monotonic probability density functions such as Mckay, Pareto and exponential distributions are also discussed by the proposed characterization techniques.   

scholarly journals Arrival Traffic Separations Modelling By Using Continuous Probability Distributions

2019 ◽  
Vol 285 ◽  
pp. 00013
Author(s):  
Adrian Pawełek ◽  
Piotr Lichota
Keyword(s):  
Mathematical Model ◽  
Quantitative Analysis ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Air Traffic ◽  
Density Functions ◽  
Traffic Intensity ◽  
Traffic Data ◽  
Model Application ◽  
Comparing Distributions

This article presents a method that allows to analyze selected aspects of past arrival traffic by modelling distributions of time separations of arriving aircraft in a chosen navigationpoint of Terminal Manoeuvring Area with the use of continuous probability distributions. Modelling arriving aircraft time separations distribution with continuous probability density functions allows to apply various mathematical tools to analyze separations distributions. Moreover, by comparing distributions parameters, quantitative analysis of separations for days with various arrival traffic intensity can be performed. Assumptions, mathematical model, application in the exemplary experimental scenario with an airport and days with low and high traffic intensity, and results are presented in this article. Real air traffic data was used for the experimental scenario. Outcomes show that the method can be used for air traffic post-analysis, e.g assessment of maintaining separation.

Using Probability Distributions in Parameters of Variables at Agent-Based Simulations

2017 ◽  
pp. 333-355
Author(s):  
Marcilene Fonseca de Moraes ◽  
Diana Francisca Adamatti ◽  
Albano Oliveira de Borba ◽  
Adriano Velasque Werhli ◽  
Andrea von Groll
Keyword(s):  
Mycobacterium Tuberculosis ◽  
Growth Curve ◽  
Probability Distributions ◽  
Agent Based ◽  
Simulation Based ◽  
Agent Based Simulations ◽  
The Rich ◽  
Rich Countries

Even treatable and preventable with medication, tuberculosis (TB) continues to infect and cause deaths globally, especially in the poorest countries and in most vulnerable parts of the rich countries. Given this situation, the study of the growth curve of Mycobacterium tuberculosis, which causes tuberculosis, can be a strong ally against TB. This study models the growth curve of Mycobacterium tuberculosis using simulation based agents, aiming to simulate the curve with the minimum possible error when compared to in vitro results. To implement this model, the agents represent the bacteria in their habitat and how they interact with each other and the environment. Some parameters of the agents are modelled with probability distributions.

The Impact of Vertical Deflection on the Ballistic Missiles for Direction and Positioning

2014 ◽  
Vol 568-570 ◽  
pp. 938-943 ◽  
Author(s):  
Jian Qiang Wang ◽  
Hua Ling Wu
Keyword(s):  
Long Range ◽  
Target Point ◽  
Impact Point ◽  
Vertical Deflection ◽  
Point Position ◽  
Simulation Based ◽  
Ballistic Missiles ◽  
The Impact

The direction and positioning of the missile could be affected by the vertical deflection which is at the launch point, so the impact point errors will increase. Based on the launch coordination, the target point position deviation formula which is caused by vertical deflection is deduced in this paper. The correction precise of the vertical deflection is also a factor of the impact point error. The simulation based on the deviation formula is conducted to analyze the affection of the vertical deflection and the correction precise of the vertical deflection. And the results show that the vertical deflection can lead to 1km error for the long range missile. In addition, if the precision of vertical deflection were improved , the impact point errors will be reduced 85m.

scholarly journals The Metalog Distributions

2016 ◽  
Vol 13 (4) ◽  
pp. 243-277 ◽  
Author(s):  
Thomas W. Keelin
Keyword(s):  
Decision Analysis ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Probability Density Functions ◽  
Cumulative Distribution ◽  
Density Functions ◽  
Creative Commons ◽  
Discrete Methods ◽  
Actual Decision ◽  
New System

The metalog distributions constitute a new system of continuous univariate probability distributions designed for flexibility, simplicity, and ease/speed of use in practice. The system is comprised of unbounded, semibounded, and bounded distributions, each of which offers nearly unlimited shape flexibility compared to previous systems of distributions. Explicit shape-flexibility comparisons are provided. Unlike other distributions that require nonlinear optimization for parameter estimation, the metalog quantile functions and probability density functions have simple closed-form expressions that are quantile parameterized linearly by cumulative-distribution-function data. Applications in fish biology and hydrology show how metalogs may aid data and distribution research by imposing fewer shape constraints than other commonly used distributions. Applications in decision analysis show how the metalog system can be specified with three assessed quantiles, how it facilities Monte Carlo simulation, and how applying it aided an actual decision that would have been made wrongly based on commonly used discrete methods. This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License. You are free to download this work and share with others for any purpose, except commercially, if you distribute your contributions under the same license as the original, and you must attribute this work as “Decision Analysis. Copyright © 2016 The Author(s). https://doi.org/10.1287/deca.2016.0338 , used under a Creative Commons Attribution License: https://creativecommons.org/licenses/by-nc-sa/4.0/ .”

scholarly journals SIMULATION-BASED PREDICTING THE POSITION OF ROAD TANK EXPLOSIONS. PART I: DATA AND MODELS

Transport ◽  
2012 ◽  
Vol 27 (1) ◽  
pp. 14-24 ◽  
Author(s):  
Egidijus Rytas Vaidogas ◽  
Lina Linkutė ◽  
Dainius Stulgys
Keyword(s):  
Thermal Effects ◽  
Probability Distributions ◽  
Study Data ◽  
Quantitative Risk Assessment ◽  
Hard Data ◽  
Rest Position ◽  
Flammable Liquids ◽  
Simulation Based ◽  
Departure Angle

Road tankers used for the transportation of flammable liquids and liquefied gases can be involved in accidents which escalate into fires and the so-called boiling liquid expanding vapour explosions. The damaging effects of these phenomena on roadside property depend on the position and orientation of exploding tanks in relation to vulnerable roadside objects. This study presents a simulation-based approach to the prediction of the position of road tank explosions. The position is expressed by longitudinal and transverse rest position of an exploding tank as well as departure angle of the tank. As a part of this study, data on transverse rest position and departure angle was collected and used to fit probability distributions which express uncertainties in these circumstantial characteristics of road tank accidents. It was found that data on the longitudinal rest position is difficult to obtain and modelling this accident characteristic will have to rely on a subjective specification of probability distributions. Such distributions can be chosen by applying approaches used in the field of quantitative risk assessment. Probability distributions, partly subjective and partly based on hard data, are applied to simulate values of potential explosion coordinates. The simulation results have the premise to be applied to forecasting mechanical and thermal effects of explosions on road and assessing damage from them. A case study used to evaluate the performance of the models proposed in this study is presented in the second part of the paper.

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