Estimation methods for the probability density function and the cumulative distribution function of the Pareto-Rayleigh distribution

Statistics ◽  
2019 ◽  
Vol 54 (1) ◽  
pp. 135-151
Author(s):  
Maleki Jebeli ◽  
E. Deiri
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Rayleigh Distribution ◽  
Cumulative Distribution ◽  
Estimation Methods

The joint asymptotic distribution of the k-smallest sample spacings

1969 ◽  
Vol 6 (02) ◽  
pp. 442-448
Author(s):  
Lionel Weiss
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Open Interval ◽  
Cumulative Distribution ◽  
The Right ◽  
Sample Spacings ◽  
Independent Identically Distributed

Suppose Q 1 ⋆, … Q n ⋆ are independent, identically distributed random variables, each with probability density function f(x), cumulative distribution function F(x), where F(1) – F(0) = 1, f(x) is continuous in the open interval (0, 1) and continuous on the right at x = 0 and on the left at x = 1, and there exists a positive C such that f(x) > C for all x in (0, l). f(0) is defined as f(0+), f(1) is defined as f(1–).

Empirical Analyses of Income: Finland (2009) and Australia (1967-1968)

2021 ◽  
pp. 35-53
Author(s):  
Johan Fellman
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Lorenz Curve ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Income Data ◽  
Difference Quotients ◽  
The Lorenz Curve

Analyses of income data are often based on assumptions concerning theoretical distributions. In this study, we apply statistical analyses, but ignore specific distribution models. The main income data sets considered in this study are taxable income in Finland (2009) and household income in Australia (1967-1968). Our intention is to compare statistical analyses performed without assumptions of the theoretical models with earlier results based on specific models. We have presented the central objects, probability density function, cumulative distribution function, the Lorenz curve, the derivative of the Lorenz curve, the Gini index and the Pietra index. The trapezium rule, Simpson´s rule, the regression model and the difference quotients yield comparable results for the Finnish data, but for the Australian data the differences are marked. For the Australian data, the discrepancies are caused by limited data. JEL classification numbers: D31, D63, E64. Keywords: Cumulative distribution function, Probability density function, Mean, quantiles, Lorenz curve, Gini coefficient, Pietra index, Robin Hood index, Trapezium rule, Simpson´s rule, Regression models, Difference quotients, Derivative of Lorenz curve

scholarly journals A NOTE CONCERNING THE DISTANCES OF UNIFORMLY DISTRIBUTED POINTS FROM THE CENTRE OF A RECTANGLE

2012 ◽  
Vol 87 (1) ◽  
pp. 115-119 ◽  
Author(s):  
ROBERT STEWART ◽  
HONG ZHANG
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Closed Form ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Average Distance ◽  
Cumulative Distribution

AbstractGiven a rectangle containing uniformly distributed random points, how far are the points from the rectangle’s centre? In this paper we provide closed-form expressions for the cumulative distribution function and probability density function that characterise the distance. An expression for the average distance to the centre of the rectangle is also provided.

scholarly journals Moments of order statistics from nonidentically Distributed Lomax, exponential Lomax and exponential Pareto Variables

2018 ◽  
Vol 14 (1) ◽  
pp. 7431-7438
Author(s):  
Nasr Ibrahim Rashwan
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Order Statistics ◽  
Density Function ◽  
Order Statistic ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Numerical Examples ◽  
Moments Of Order Statistics

In this paper, the probability density function and the cumulative distribution function of the rth order statistic arising from independent nonidentically distributed (INID) Lomax, exponential Lomax and exponential Pareto variables are presented. The moments of order statistics from INID Lomax, exponential lomax and exponential Pareto were derived using the technique established by Barakat and Abdelkader. Also, numerical examples are given.

scholarly journals Evolution of bioacoustic correlometers: from setups for analysis of probability density function (PDF), cumulative distribution function (CDF), [spectral] entropy of signal (SE) & quality of masking noise (QMN) to palmtop-like pocket devices

2019 ◽  
Author(s):  
Oleg Gradov ◽  
Eugene Adamovich ◽  
Serge Pankratov
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Spectral Entropy ◽  
Masking Noise ◽  
Probability Density Function Pdf

Evolution of bioacoustic correlometers: from setups for analysis of probability density function (PDF), cumulative distribution function (CDF), [spectral] entropy of signal (SE) & quality of masking noise (QMN) to palmtop-like pocket devices Novel references:

The joint asymptotic distribution of the k-smallest sample spacings

1969 ◽  
Vol 6 (2) ◽  
pp. 442-448 ◽  
Author(s):  
Lionel Weiss
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Open Interval ◽  
Cumulative Distribution ◽  
The Right ◽  
Sample Spacings ◽  
Independent Identically Distributed

Suppose Q1⋆, … Qn⋆ are independent, identically distributed random variables, each with probability density function f(x), cumulative distribution function F(x), where F(1) – F(0) = 1, f(x) is continuous in the open interval (0, 1) and continuous on the right at x = 0 and on the left at x = 1, and there exists a positive C such that f(x) > C for all x in (0, l). f(0) is defined as f(0+), f(1) is defined as f(1–).

scholarly journals Some Generalized Inequalities Involving Local Fractional Integrals and their Applications for Random Variables and Numerical Integration

2016 ◽  
Vol 12 (2) ◽  
pp. 49-65 ◽  
Author(s):  
S. Erden ◽  
M. Z. Sarikaya ◽  
N. Çelik
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Numerical Integration ◽  
Density Function ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Fractional Integrals ◽  
Grüss Inequality

Abstract We establish generalized pre-Grüss inequality for local fractional integrals. Then, we obtain some inequalities involving generalized expectation, p−moment, variance and cumulative distribution function of random variable whose probability density function is bounded. Finally, some applications for generalized Ostrowski-Grüss inequality in numerical integration are given.

Fourier Transforms in Probability, Random Variables and Stochastic Processes

2009 ◽  
Author(s):  
Robert J Marks II
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Fourier Analysis ◽  
Stochastic Processes ◽  
Probability Density ◽  
Density Function ◽  
Fourier Transforms ◽  
Random Variables ◽  
Cumulative Distribution ◽  
The Face

In this Chapter, we present application of Fourier analysis to probability, random variables and stochastic processes [1089, 1097, 1387, 1329]. Arandom variable, X, is the assignment of a number to the outcome of a random experiment. We can, for example, flip a coin and assign an outcome of a heads as X = 1 and a tails X = 0. Often the number is equated to the numerical outcome of the experiment, such as the number of dots on the face of a rolled die or the measurement of a voltage in a noisy circuit. The cumulative distribution function is defined by FX(x) = Pr[X ≤ x]. (4.1) The probability density function is the derivative fX(x) = d /dxFX(x). Our treatment of random variables focuses on use of Fourier analysis. Due to this viewpoint, the development we use is unconventional and begins immediately in the next section with discussion of properties of the probability density function.

scholarly journals Hypergeometric Functions on Cumulative Distribution Function

2019 ◽  
pp. 1-11
Author(s):  
Pooja Singh
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Probability Density ◽  
Hypergeometric Function ◽  
Hypergeometric Functions ◽  
Cumulative Distribution Function ◽  
Cumulative Distribution ◽  
Unified Approach ◽  
Exponential Functions ◽  
Chi Square

Exponential functions have been extended to Hypergeometric functions. There are many functions which can be expressed in hypergeometric function by using its analytic properties. In this paper, we will apply a unified approach to the probability density function and corresponding cumulative distribution function of the noncentral chi square variate to extract and derive hypergeometric functions.

Properties and methods of estimation for a bivariate exponentiated Fréchet distribution

2020 ◽  
Vol 70 (5) ◽  
pp. 1211-1230
Author(s):  
Abdus Saboor ◽  
Hassan S. Bakouch ◽  
Fernando A. Moala ◽  
Sheraz Hussain
Keyword(s):  
Maximum Likelihood ◽  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Superior Performance ◽  
Estimation Methods ◽  
Conditional Probability Density ◽  
Data Set ◽  
Fréchet Distribution ◽  
Frechet Distribution

AbstractIn this paper, a bivariate extension of exponentiated Fréchet distribution is introduced, namely a bivariate exponentiated Fréchet (BvEF) distribution whose marginals are univariate exponentiated Fréchet distribution. Several properties of the proposed distribution are discussed, such as the joint survival function, joint probability density function, marginal probability density function, conditional probability density function, moments, marginal and bivariate moment generating functions. Moreover, the proposed distribution is obtained by the Marshall-Olkin survival copula. Estimation of the parameters is investigated by the maximum likelihood with the observed information matrix. In addition to the maximum likelihood estimation method, we consider the Bayesian inference and least square estimation and compare these three methodologies for the BvEF. A simulation study is carried out to compare the performance of the estimators by the presented estimation methods. The proposed bivariate distribution with other related bivariate distributions are fitted to a real-life paired data set. It is shown that, the BvEF distribution has a superior performance among the compared distributions using several tests of goodness–of–fit.

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