scholarly journals A Skewed Model Combining Triangular and Exponential Features: The Two-faced Distribution and its Statistical Properties

2016 ◽  
Vol 35 (4) ◽  
Author(s):  
Maurizio Brizzi
Keyword(s):  
Distribution Function ◽  
Parameter Estimation ◽  
Goodness Of Fit ◽  
Cumulative Distribution Function ◽  
Continuous Distribution ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Model Combining ◽  
Left And Right ◽  
Expected Values

A new continuous distribution model is introduced, joining triangular and exponential features, respectively on the left and right side of a hinge point. The cumulative distribution function is derived, as well as the first three moments. Expected values and the Pearson index of skewness are tabulated. A possible step-by-step approach to parameter estimation is outlined. An application to Italian geographical data is given, referring to a set of municipalities classified by population, showing a very satisfactory goodness of fit.

scholarly journals Results of the Verification of the Statistical Distribution Model of Microseismicity Emission Characteristics

2016 ◽  
Vol 61 (3) ◽  
pp. 489-496
Author(s):  
Aleksander Cianciara
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Goodness Of Fit ◽  
Cumulative Distribution Function ◽  
Statistical Distribution ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Emission Characteristics ◽  
Goodness Of Fit Test ◽  
Empirical Cumulative Distribution Function

Abstract The paper presents the results of research aimed at verifying the hypothesis that the Weibull distribution is an appropriate statistical distribution model of microseismicity emission characteristics, namely: energy of phenomena and inter-event time. It is understood that the emission under consideration is induced by the natural rock mass fracturing. Because the recorded emission contain noise, therefore, it is subjected to an appropriate filtering. The study has been conducted using the method of statistical verification of null hypothesis that the Weibull distribution fits the empirical cumulative distribution function. As the model describing the cumulative distribution function is given in an analytical form, its verification may be performed using the Kolmogorov-Smirnov goodness-of-fit test. Interpretations by means of probabilistic methods require specifying the correct model describing the statistical distribution of data. Because in these methods measurement data are not used directly, but their statistical distributions, e.g., in the method based on the hazard analysis, or in that that uses maximum value statistics.

scholarly journals ANALISIS KUMULATIF COVID-19 PROVINSI PAPUA TAHUN 2020 MENGGUNAKAN MODEL DISTRIBUSI JOHNSON SB

2021 ◽  
Vol 21 (1) ◽  
pp. 21-28
Author(s):  
Felix Reba ◽  
Alvian Sroyer
Keyword(s):  
Distribution Function ◽  
Maximum Likelihood ◽  
Cumulative Distribution Function ◽  
Data Distribution ◽  
Secondary Data ◽  
Cumulative Distribution ◽  
Distribution Model ◽  
Cumulative Probability ◽  
Number Of Patients ◽  
Kolmogorov Smirnov

Coronavirus belongs to the coronaviridae family. The coronavirus family groups are alpha (α), beta (β), gamma (γ) and delta (δ) coronavirus. Although research related to covid-19 in several provinces in Indonesia has been conducted by several researchers so far there has been no research related to the Covid-19 model in Papua province. One of the obstacles faced by some researchers is related to the Covid-19 data parameters which are difficult to estimate, so that the model formulated could not describe the outbreak well. Therefore the aim of this study is to conduct a cumulative analysis of the 2020 Papua province Covid-19 using the Johnson SB distribution model. The methods used to perform the analysis are Kolmogorov Smirnov for testing the suitability of the Covid-19 data to the model, Johnson SB to show the data distribution model, Maximum Likelihood to estimate the parameters and the Johnson SB cumulative distribution function to describe the probability of Covid-19 data. 19 Papua Province in 2020. The secondary data on the number of Covid-19 cases in Papua, obtained from the Papua Provincial Health Office is used in this research. The results showed that, the highest increase in the number of patients every day, starting from September 1 2020 to October 31, 2020 for infected cases was on 16-17 September, by 274 patients. Meanwhile, most recovery (308 patients) happened to be on 30-31 October and the highest death (5 people) was on 27-28 September. The highest cumulative probability for cases of infection, recovery and death were (Confirmed <4965) = 0.3, Prob(Cured <6408) = 0.9 and Prob(died <91) = 0.4 respectively.

scholarly journals On a New Result on the Ratio Exponentiated General Family of Distributions with Applications

Mathematics ◽  
2020 ◽  
Vol 8 (4) ◽  
pp. 598 ◽  
Author(s):  
Rashad A. R. Bantan ◽  
Farrukh Jamal ◽  
Christophe Chesneau ◽  
Mohammed Elgarhy
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Natural Extension ◽  
Continuous Distribution ◽  
Cumulative Distribution ◽  
Likelihood Method ◽  
Model Parameters ◽  
Mathematical Treatment ◽  
General Family ◽  
Family Of Distributions

In this paper, we first show a new probability result which can be concisely formulated as follows: the function 2 G β / ( 1 + G α ) , where G denotes a baseline cumulative distribution function of a continuous distribution, can have the properties of a cumulative distribution function beyond the standard assumptions on α and β (possibly different and negative, among others). Then, we provide a complete mathematical treatment of the corresponding family of distributions, called the ratio exponentiated general family. To link it with the existing literature, it constitutes a natural extension of the type II half logistic-G family or, from another point of view, a compromise between the so-called exponentiated-G and Marshall-Olkin-G families. We show that it possesses tractable probability functions, desirable stochastic ordering properties and simple analytical expressions for the moments, among others. Also, it reaches high levels of flexibility in a wide statistical sense, mainly thanks to the wide ranges of possible values for α and β and thus, can be used quite effectively for the real data analysis. We illustrate this last point by considering the Weibull distribution as baseline and three practical data sets, with estimation of the model parameters by the maximum likelihood method.

scholarly journals Parameter Estimation Techniques Based on Optimizing Goodness-of-Fit Statistics for Structural Reliability

1993 ◽  
Author(s):  
Alois Starlinger ◽  
Stephen F. Duffy ◽  
Joseph L. Palko
Keyword(s):  
Distribution Function ◽  
Goodness Of Fit ◽  
Cumulative Distribution Function ◽  
Structural Reliability ◽  
Empirical Distribution ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Weibull Parameters ◽  
Fit Statistics ◽  
Failure Data

Abstract New methods are presented that utilize the optimization of goodness-of-fit statistics in order to estimate Weibull parameters from failure data. It is assumed that the underlying population is characterized by a three-parameter Weibull distribution. Goodness-of-fit tests are based on the empirical distribution function (EDF). The EDF is a step function, calculated using failure data, and represents an approximation of the cumulative distribution function for the underlying population. Statistics (such as the Kolmogorov-Smirnov statistic and the Anderson-Darling statistic) measure the discrepancy between the EDF and the cumulative distribution function (CDF). These statistics are minimized with respect to the three Weibull parameters. Due to nonlinearities encountered in the minimization process, Powell’s numerical optimization procedure is applied to obtain the optimum value of the EDF. Numerical examples show the applicability of these new estimation methods. The results are compared to the estimates obtained with Cooper’s nonlinear regression algorithm.

DISSONANCE — A MEASURE OF VARIABILITY FOR ORDINAL RANDOM VARIABLES

2001 ◽  
Vol 09 (01) ◽  
pp. 39-53 ◽  
Author(s):  
RONALD R. YAGER
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Probability Distributions ◽  
Random Variables ◽  
Cumulative Distribution ◽  
General Properties

We look at the issue of obtaining a variance like measure associated with probability distributions over ordinal sets. We call these dissonance measures. We specify some general properties desired in these dissonance measures. The centrality of the cumulative distribution function in formulating the concept of dissonance is pointed out. We introduce some specific examples of measures of dissonance.

Estimating the cumulative distribution function for the linear combination of gamma random variables

2017 ◽  
Vol 20 (5) ◽  
pp. 939-951
Author(s):  
Amal Almarwani ◽  
Bashair Aljohani ◽  
Rasha Almutairi ◽  
Nada Albalawi ◽  
Alya O. Al Mutairi
Keyword(s):  
Distribution Function ◽  
Linear Combination ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Cumulative Distribution
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