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.

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–).

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 Modified Weighted Pareto Distribution Type I (MWPDTI)

2020 ◽  
Vol 17 (3) ◽  
pp. 0869
Author(s):  
Mahmood A. Sahmran
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Density Function ◽  
Pareto Distribution ◽  
Random Variable ◽  
Reliability Function ◽  
Cumulative Distribution ◽  
Type I ◽  
Standard Distribution ◽  
Distribution Type

In this paper, the Azzallini’s method used to find a weighted distribution derived from the standard Pareto distribution of type I (SPDTI) by inserting the shape parameter (θ) resulting from the above method to cover the period (0, 1] which was neglected by the standard distribution. Thus, the proposed distribution is a modification to the Pareto distribution of the first type, where the probability of the random variable lies within the period  The properties of the modified weighted Pareto distribution of the type I (MWPDTI) as the probability density function ,cumulative distribution function, Reliability function , Moment and  the hazard function are found. The behaviour of probability density function for MWPDTI distribution by representing the values of    This means, the probability density function of this distribution treats the period (0,1] which is ignore in SPDTI.

scholarly journals Estimasi Fungsi Survival dan Fungsi Hazard Kumulatif Pada Data Survival Pederita Multiple Myeloma Serta Faktor-faktor yang Mempengaruhi Waktu Survivalnya

Intersections ◽  
2019 ◽  
Vol 4 (2) ◽  
pp. 33-43
Author(s):  
Toto Hermawan ◽  
Dwi Nurrohmah ◽  
Ismi Fathul Jannah
Keyword(s):  
Multiple Myeloma ◽  
Distribution Function ◽  
Data Analysis ◽  
Probability Density Function ◽  
Weibull Distribution ◽  
Hazard Function ◽  
Cumulative Distribution Function ◽  
Survival Function ◽  
Random Variable ◽  
Cumulative Distribution

Multiple myeloma is an infectious disease characterized by the accumulation of abnormal plasma cells, a type of white blood cell, in the bone marrow. The main objective of this data analysis is to investigate the effect of Bun, Ca, Pcells and Protein risk factors on the survival time of multiple myeloma patients from diagnosis to death. In the survival data analysis, the observed random variable T is the time needed to achieve success. To explain a random variable, the cumulative distribution function or the probability density function can be used. In survival analysis, the function of the random variable that becomes important is the survival function and the hazard function which can be derived using the cumulative distribution function or the probability density function. In general, it is difficult to determine the survival function or hazard function of a population group with certainty. However, the survival function or hazard function can still be approximated by certain estimation methods. The Kaplan-Meier method can be used to find estimators of the survival function of a population. Meanwhile, to find the estimator of the cumuative hazard function, the Nelson-Aalen method can be used. From the variables studied, it turned out that the one that gave the most significant effect was the Bun variable, namely blood urea nitrogen levels using both the exponential and weibull distribution. However, by using the weibull distribution, the presence of Bence Jones Protein in urine also has a quite real effect

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