A New Characterization of Exponential Distribution through Minimum Chi-Squared Divergence Principle

2020 ◽  
Vol 05 (1&2) ◽  
pp. 14-26
Author(s):  
Amr Ragab Rabie Kamel ◽  
Keyword(s):  
Exponential Distribution ◽  
Probability Distributions ◽  
Special Values ◽  
Chi Squared ◽  
Available Information

In this paper, a new characterizing theorems of exponential distribution based on minimum chi-Squared divergence principle are presented. We study minimum chi-squared divergence probability distributions by this principle given a prior exponential distribution and the available information on moments. Some illustrative examples are included for special values of the parameters. We tabulated the results and the corresponding characteristics of the distribution are graphically, compared.

scholarly journals On revelation transforms that characterize probability distributions

1993 ◽  
Vol 6 (4) ◽  
pp. 345-357 ◽  
Author(s):  
S. Chukova ◽  
B. Dimitrov ◽  
J.-P. Dion
Keyword(s):  
Exponential Distribution ◽  
Probability Distributions ◽  
Random Variables ◽  
Memory Property ◽  
Lack Of Memory Property

A characterization of exponential, geometric and of distributions with almost-lack-of-memory property, based on the “revelation transform of probability distributions” and “relevation of random variables” is discussed. Known characterizations of the exponential distribution on the base of relevation transforms given by Grosswald et al. [4], and Lau and Rao [7] are obtained under weakened conditions and the proofs are simplified. A characterization the class of almost-lack-of-memory distributions through the relevation is specified.

scholarly journals A Brief Review of Generalized Entropies

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 813 ◽  
Author(s):  
José Amigó ◽  
Sámuel Balogh ◽  
Sergio Hernández
Keyword(s):  
Diffusion Processes ◽  
Complex Dynamics ◽  
Probability Distributions ◽  
Point Of View ◽  
Scaling Exponent ◽  
Scaling Exponents ◽  
Physical Systems ◽  
New Phenomena ◽  
Generalized Entropies

Entropy appears in many contexts (thermodynamics, statistical mechanics, information theory, measure-preserving dynamical systems, topological dynamics, etc.) as a measure of different properties (energy that cannot produce work, disorder, uncertainty, randomness, complexity, etc.). In this review, we focus on the so-called generalized entropies, which from a mathematical point of view are nonnegative functions defined on probability distributions that satisfy the first three Shannon–Khinchin axioms: continuity, maximality and expansibility. While these three axioms are expected to be satisfied by all macroscopic physical systems, the fourth axiom (separability or strong additivity) is in general violated by non-ergodic systems with long range forces, this having been the main reason for exploring weaker axiomatic settings. Currently, non-additive generalized entropies are being used also to study new phenomena in complex dynamics (multifractality), quantum systems (entanglement), soft sciences, and more. Besides going through the axiomatic framework, we review the characterization of generalized entropies via two scaling exponents introduced by Hanel and Thurner. In turn, the first of these exponents is related to the diffusion scaling exponent of diffusion processes, as we also discuss. Applications are addressed as the description of the main generalized entropies advances.

A Characterization of the Exponential Distribution

1994 ◽  
Vol 44 (1-2) ◽  
pp. 123-126
Author(s):  
E. S. Jebvanand ◽  
N. Unnikrishnan Nair
Keyword(s):  
Exponential Distribution ◽  
Prior Distribution ◽  
Future Observation ◽  
Informative Prior ◽  
Informative Prior Distribution ◽  
Continuous Population

In this note we prove that the exponential distribution is characterized by the property [Formula: see text] where Y is a future observation and x1, x2,…, x n are identical and independently distributed observations from a continuous population with density f( x; a), where a is assumed to have a non-informative prior distribution

scholarly journals Integrating macroseismic intensity distributions with a probabilistic approach: an application in Italy

2021 ◽  
Vol 21 (8) ◽  
pp. 2299-2311
Author(s):  
Andrea Antonucci ◽  
Andrea Rovida ◽  
Vera D'Amico ◽  
Dario Albarello
Keyword(s):  
Southern Italy ◽  
Central Italy ◽  
Probabilistic Approach ◽  
Source Characterization ◽  
Strong Earthquakes ◽  
Intensity Prediction ◽  
Macroseismic Intensities ◽  
Earthquake Effects ◽  
Available Information

Abstract. The geographic distribution of earthquake effects quantified in terms of macroseismic intensities, the so-called macroseismic field, provides basic information for several applications including source characterization of pre-instrumental earthquakes and risk analysis. Macroseismic fields of past earthquakes as inferred from historical documentation may present spatial gaps, due to the incompleteness of the available information. We present a probabilistic approach aimed at integrating incomplete intensity distributions by considering the Bayesian combination of estimates provided by intensity prediction equations (IPEs) and data documented at nearby localities, accounting for the relevant uncertainties and the discrete and ordinal nature of intensity values. The performance of the proposed methodology is tested at 28 Italian localities with long and rich seismic histories and for two well-known strong earthquakes (i.e., 1980 southern Italy and 2009 central Italy events). A possible application of the approach is also illustrated relative to a 16th-century earthquake in the northern Apennines.

scholarly journals Probability distributions of COVID-19 tweet posted trends use a nonhomogeneous Poisson process

2020 ◽  
Vol 1 (4) ◽  
pp. 229-238
Author(s):  
Devi Munandar ◽  
Sudradjat Supian ◽  
Subiyanto Subiyanto
Keyword(s):  
Social Media ◽  
Poisson Process ◽  
Exponential Distribution ◽  
Probability Distributions ◽  
Nonhomogeneous Poisson Process ◽  
Time Interval ◽  
Initial State ◽  
Time Intervals ◽  
Time Parameters ◽  
Parameter Values

The influence of social media in disseminating information, especially during the COVID-19 pandemic, can be observed with time interval, so that the probability of number of tweets discussed by netizens on social media can be observed. The nonhomogeneous Poisson process (NHPP) is a Poisson process dependent on time parameters and the exponential distribution having unequal parameter values and, independently of each other. The probability of no occurrence an event in the initial state is one and the probability of an event in initial state is zero. Using of non-homogeneous Poisson in this paper aims to predict and count the number of tweet posts with the keyword coronavirus, COVID-19 with set time intervals every day. Posting of tweets from one time each day to the next do not affect each other and the number of tweets is not the same. The dataset used in this study is crawling of COVID-19 tweets three times a day with duration of 20 minutes each crawled for 13 days or 39 time intervals. The result of this study obtained predictions and calculated for the probability of the number of tweets for the tendency of netizens to post on the situation of the COVID-19 pandemic.

A characterization of the negative exponential distribution with application to reliability theory

1981 ◽  
Vol 18 (3) ◽  
pp. 652-659 ◽  
Author(s):  
M. J. Phillips
Keyword(s):  
Exponential Distribution ◽  
Random Variables ◽  
Reliability Theory ◽  
The Other ◽  
Independent Random Variables ◽  
System Availability ◽  
Failure Times ◽  
Negative Exponential Distribution ◽  
Negative Exponential

The negative exponential distribution is characterized in terms of two independent random variables. Only one of the random variables has a negative exponential distribution whilst the other can belong to a wide class of distributions. This result is then applied to two models for the reliability of a system of two modules subject to revealed and unrevealed faults to show when the models are equivalent. It is also shown, under certain conditions, that the system availability is only independent of the distribution of revealed failure times in one module when unrevealed failure times in the other module have a negative exponential distribution.

Sign in / Sign up

Export Citation Format

Share Document