On Log-q-Gaussian Distribution

2018 ◽  
Vol 70 (2) ◽  
pp. 105-121
Author(s):  
Ken-ichi Koike ◽  
Yuya Shimegi
Keyword(s):  
Distribution Function ◽  
Gaussian Distribution ◽  
Cumulative Distribution Function ◽  
Extreme Value Distribution ◽  
Likelihood Estimation ◽  
Real Data ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Ams Classification ◽  
New Distribution

We propose the log- q-Gaussian distribution which is obtained as the distribution of a random variable whose logarithm is q-Gaussian. Various types of properties of the new distribution are given such as the moments, the cumulative distribution function, the extreme value distribution, the likelihood estimation, and so on. Some examples for real data are also given. AMS Classification: 60Exx 62Exx.

scholarly journals On the Properties and Applications of Transmuted Odd Generalized Exponential-Exponential Distribution

2018 ◽  
pp. 1-14
Author(s):  
Jamila Abdullahi ◽  
Umar Kabir Abdullahi ◽  
Terna Godfrey Ieren ◽  
David Adugh Kuhe ◽  
Adamu Abubakar Umar
Keyword(s):  
Distribution Function ◽  
Probability Density Function ◽  
Exponential Distribution ◽  
Cumulative Distribution Function ◽  
Real Life ◽  
Likelihood Estimation ◽  
Cumulative Distribution ◽  
Method Of Maximum Likelihood ◽  
Probability Density Function Pdf ◽  
New Distribution

This article proposed a new distribution referred to as the transmuted odd generalized exponential-exponential distribution (TOGEED) as an extension of the popular odd generalized exponential- exponential distribution by using the Quadratic rank transmutation map (QRTM) proposed and studied by [1]. Using the transmutation map, we defined the probability density function (pdf) and cumulative distribution function (cdf) of the transmuted odd generalized Exponential- Exponential distribution. Some properties of the new distribution were extensively studied after derivation. The estimation of the distribution’s parameters was also done using the method of maximum likelihood estimation. The performance of the proposed probability distribution was checked in comparison with some other generalizations of Exponential distribution using a real life dataset.  

scholarly journals On Distribution Characteristics of a Fuzzy Random Variable

2018 ◽  
Vol 47 (2) ◽  
pp. 53-67 ◽  
Author(s):  
Jalal Chachi
Keyword(s):  
Probability Theory ◽  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variables ◽  
Fuzzy Random Variable ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Distribution Characteristics ◽  
Fuzzy Random Variables ◽  
Fuzzy Random

In this paper, rst a new notion of fuzzy random variables is introduced. Then, usingclassical techniques in Probability Theory, some aspects and results associated to a randomvariable (including expectation, variance, covariance, correlation coecient, etc.) will beextended to this new environment. Furthermore, within this framework, we can use thetools of general Probability Theory to dene fuzzy cumulative distribution function of afuzzy random variable.

scholarly journals Closed form expressions for moments of the beta Weibull distribution

2011 ◽  
Vol 83 (2) ◽  
pp. 357-373 ◽  
Author(s):  
Gauss M Cordeiro ◽  
Alexandre B Simas ◽  
Borko D Stošic
Keyword(s):  
Weibull Distribution ◽  
Closed Form ◽  
Cumulative Distribution Function ◽  
Information Matrix ◽  
Likelihood Estimation ◽  
Real Data ◽  
Cumulative Distribution ◽  
Data Set ◽  
Expected Information ◽  
Beta Weibull Distribution

The beta Weibull distribution was first introduced by Famoye et al. (2005) and studied by these authors and Lee et al. (2007). However, they do not give explicit expressions for the moments. In this article, we derive explicit closed form expressions for the moments of this distribution, which generalize results available in the literature for some sub-models. We also obtain expansions for the cumulative distribution function and Rényi entropy. Further, we discuss maximum likelihood estimation and provide formulae for the elements of the expected information matrix. We also demonstrate the usefulness of this distribution on a real data set.

scholarly journals Nondecreasing Lower Bound on the Poisson Cumulative Distribution Function for z Standard Deviations Above the Mean

2013 ◽  
Vol 50 (4) ◽  
pp. 909-917
Author(s):  
M. Bondareva
Keyword(s):  
Distribution Function ◽  
Lower Bound ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Step Function ◽  
Cumulative Distribution ◽  
Control Parameters ◽  
Poisson Random Variable ◽  
The Mean ◽  
Standard Deviations

In this paper we discuss a nondecreasing lower bound for the Poisson cumulative distribution function (CDF) at z standard deviations above the mean λ, where z and λ are parameters. This is important because the normal distribution as an approximation for the Poisson CDF may overestimate or underestimate its value. A sharp nondecreasing lower bound in the form of a step function is constructed. As a corollary of the bound's properties, for a given percent α and parameter λ, the minimal z is obtained such that, for any Poisson random variable with the mean greater or equal to λ, its αth percentile is at most z standard deviations above its mean. For Poisson distributed control parameters, the corollary allows simple policies measuring performance in terms of standard deviations from a benchmark.

NONPARAMETRIC KERNEL DISTRIBUTION FUNCTION ESTIMATION NEAR ENDPOINTS

2021 ◽  
Vol 10 (12) ◽  
pp. 3679-3697
Author(s):  
N. Almi ◽  
A. Sayah
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Kernel Estimator ◽  
Real Data ◽  
Cumulative Distribution ◽  
Function Estimation ◽  
Distribution Function Estimation ◽  
The Right ◽  
Nonparametric Kernel ◽  
Better Than

In this paper, two kernel cumulative distribution function estimators are introduced and investigated in order to improve the boundary effects, we will restrict our attention to the right boundary. The first estimator uses a self-elimination between modify theoretical Bias term and the classical kernel estimator itself. The basic technique of construction the second estimator is kind of a generalized reflection method involving reflection a transformation of the observed data. The theoretical properties of our estimators turned out that the Bias has been reduced to the second power of the bandwidth, simulation studies and two real data applications were carried out to check these phenomena and are conducted that the proposed estimators are better than the existing boundary correction methods.

ON CUMULATIVE RESIDUAL EXTROPY

2019 ◽  
Vol 34 (4) ◽  
pp. 605-625 ◽  
Author(s):  
S. M. A. Jahanshahi ◽  
H. Zarei ◽  
A. H. Khammar
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Cumulative Distribution ◽  
Alternative Measure ◽  
Numerical Examples ◽  
Cumulative Residual ◽  
Measure Of Uncertainty

Recently, an alternative measure of uncertainty called extropy is proposed by Lad et al. [12]. The extropy is a dual of entropy which has been considered by researchers. In this article, we introduce an alternative measure of uncertainty of random variable which we call it cumulative residual extropy. This measure is based on the cumulative distribution function F. Some properties of the proposed measure, such as its estimation and applications, are studied. Finally, some numerical examples for illustrating the theory are included.

A Simplification and Implementation of Random-effects Meta-analyses Based on the Exact Distribution of Cochran’s Q

2014 ◽  
Vol 53 (01) ◽  
pp. 54-61 ◽  
Author(s):  
M. Preuß ◽  
A. Ziegler
Keyword(s):  
Distribution Function ◽  
Cumulative Distribution Function ◽  
Type I Error ◽  
Meta Analysis ◽  
Real Data ◽  
R Package ◽  
Cumulative Distribution ◽  
Data Sets ◽  
Type I ◽  
Simulation Studies

SummaryBackground: The random-effects (RE) model is the standard choice for meta-analysis in the presence of heterogeneity, and the stand ard RE method is the DerSimonian and Laird (DSL) approach, where the degree of heterogeneity is estimated using a moment-estimator. The DSL approach does not take into account the variability of the estimated heterogeneity variance in the estimation of Cochran’s Q. Biggerstaff and Jackson derived the exact cumulative distribution function (CDF) of Q to account for the variability of Ť 2.Objectives: The first objective is to show that the explicit numerical computation of the density function of Cochran’s Q is not required. The second objective is to develop an R package with the possibility to easily calculate the classical RE method and the new exact RE method.Methods: The novel approach was validated in extensive simulation studies. The different approaches used in the simulation studies, including the exact weights RE meta-analysis, the I 2 and T 2 estimates together with their confidence intervals were implemented in the R package metaxa.Results: The comparison with the classical DSL method showed that the exact weights RE meta-analysis kept the nominal type I error level better and that it had greater power in case of many small studies and a single large study. The Hedges RE approach had inflated type I error levels. Another advantage of the exact weights RE meta-analysis is that an exact confidence interval for T 2is readily available. The exact weights RE approach had greater power in case of few studies, while the restricted maximum likelihood (REML) approach was superior in case of a large number of studies. Differences between the exact weights RE meta-analysis and the DSL approach were observed in the re-analysis of real data sets. Application of the exact weights RE meta-analysis, REML, and the DSL approach to real data sets showed that conclusions between these methods differed.Conclusions: The simplification does not require the calculation of the density of Cochran’s Q, but only the calculation of the cumulative distribution function, while the previous approach required the computation of both the density and the cumulative distribution function. It thus reduces computation time, improves numerical stability, and reduces the approximation error in meta-analysis. The different approaches, including the exact weights RE meta-analysis, the I 2 and T 2estimates together with their confidence intervals are available in the R package metaxa, which can be used in applications.

Nondecreasing Lower Bound on the Poisson Cumulative Distribution Function for z Standard Deviations Above the Mean

2013 ◽  
Vol 50 (04) ◽  
pp. 909-917
Author(s):  
M. Bondareva
Keyword(s):  
Distribution Function ◽  
Lower Bound ◽  
Cumulative Distribution Function ◽  
Random Variable ◽  
Step Function ◽  
Cumulative Distribution ◽  
Control Parameters ◽  
Poisson Random Variable ◽  
The Mean ◽  
Standard Deviations

In this paper we discuss a nondecreasing lower bound for the Poisson cumulative distribution function (CDF) at z standard deviations above the mean λ, where z and λ are parameters. This is important because the normal distribution as an approximation for the Poisson CDF may overestimate or underestimate its value. A sharp nondecreasing lower bound in the form of a step function is constructed. As a corollary of the bound's properties, for a given percent α and parameter λ, the minimal z is obtained such that, for any Poisson random variable with the mean greater or equal to λ, its αth percentile is at most z standard deviations above its mean. For Poisson distributed control parameters, the corollary allows simple policies measuring performance in terms of standard deviations from a benchmark.

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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