scholarly journals The Parameter Estimation of the Mixture of Normal and Uniform Distribution Based on the Empirical Cumulative Distribution Function

2016 ◽  
Vol 05 (03) ◽  
pp. 237-245
Author(s):  
小英 王
Keyword(s):  
Distribution Function ◽  
Parameter Estimation ◽  
Uniform Distribution ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Empirical Cumulative Distribution Function

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 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 On the Generalized Lognormal Distribution

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Thomas L. Toulias ◽  
Christos P. Kitsos
Keyword(s):  
Distribution Function ◽  
Uniform Distribution ◽  
Series Expansion ◽  
Lognormal Distribution ◽  
Cumulative Distribution Function ◽  
Shape Parameter ◽  
Error Function ◽  
Cumulative Distribution ◽  
Dirac Distribution

This paper introduces, investigates, and discusses the -order generalized lognormal distribution (-GLD). Under certain values of the extra shape parameter , the usual lognormal, log-Laplace, and log-uniform distribution, are obtained, as well as the degenerate Dirac distribution. The shape of all the members of the -GLD family is extensively discussed. The cumulative distribution function is evaluated through the generalized error function, while series expansion forms are derived. Moreover, the moments for the -GLD are also studied.

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