scholarly journals Contracting and Involutive Negations of Probability Distributions

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2389
Author(s):  
Ildar Z. Batyrshin
Keyword(s):  
Fuzzy Logic ◽  
Uniform Distribution ◽  
Open Problem ◽  
Probability Distributions ◽  
Maximal Entropy ◽  
Involutive Negation

A dozen papers have considered the concept of negation of probability distributions (pd) introduced by Yager. Usually, such negations are generated point-by-point by functions defined on a set of probability values and called here negators. Recently the class of pd-independent linear negators has been introduced and characterized using Yager’s negator. The open problem was how to introduce involutive negators generating involutive negations of pd. To solve this problem, we extend the concepts of contracting and involutive negations studied in fuzzy logic on probability distributions. First, we prove that the sequence of multiple negations of pd generated by a linear negator converges to the uniform distribution with maximal entropy. Then, we show that any pd-independent negator is non-involutive, and any non-trivial linear negator is strictly contracting. Finally, we introduce an involutive negator in the class of pd-dependent negators. It generates an involutive negation of probability distributions.

scholarly journals A note about the uniform distribution on the intersection of a simplex and a sphere

2017 ◽  
Vol 09 (04) ◽  
pp. 717-738 ◽  
Author(s):  
Sourav Chatterjee
Keyword(s):  
Phase Transitions ◽  
Uniform Distribution ◽  
Probability Distributions ◽  
High Dimensions ◽  
Uniform Probability ◽  
Product Measures

Uniform probability distributions on [Formula: see text] balls and spheres have been studied extensively and are known to behave like product measures in high dimensions. In this note we consider the uniform distribution on the intersection of a simplex and a sphere. Certain new and interesting features, such as phase transitions and localization phenomena emerge.

scholarly journals Optimization results for a generalized coupon collector problem

2016 ◽  
Vol 53 (2) ◽  
pp. 622-629 ◽  
Author(s):  
Emmanuelle Anceaume ◽  
Yann Busnel ◽  
Ernst Schulte-Geers ◽  
Bruno Sericola
Keyword(s):  
Probability Distribution ◽  
Uniform Distribution ◽  
Closed Subset ◽  
Probability Distributions ◽  
Fixed Number ◽  
Coupon Collector ◽  
The One

Abstract In this paper we study a generalized coupon collector problem, which consists of analyzing the time needed to collect a given number of distinct coupons that are drawn from a set of coupons with an arbitrary probability distribution. We suppose that a special coupon called the null coupon can be drawn but never belongs to any collection. In this context, we prove that the almost uniform distribution, for which all the nonnull coupons have the same drawing probability, is the distribution which stochastically minimizes the time needed to collect a fixed number of distinct coupons. Moreover, we show that in a given closed subset of probability distributions, the distribution with all its entries, but one, equal to the smallest possible value is the one which stochastically maximizes the time needed to collect a fixed number of distinct coupons.

scholarly journals Family of probability distributions derived from maximal entropy principle with scale invariant restrictions

2013 ◽  
Vol 87 (1) ◽  
Author(s):  
Giorgio Sonnino ◽  
György Steinbrecher ◽  
Alessandro Cardinali ◽  
Alberto Sonnino ◽  
Mustapha Tlidi
Keyword(s):  
Probability Distributions ◽  
Maximal Entropy ◽  
Scale Invariant ◽  
Entropy Principle

A Poincaré limit theorem for wrapped probability distributions on compact symmetric spaces

1984 ◽  
Vol 95 (2) ◽  
pp. 329-334
Author(s):  
P. E. Jupp
Keyword(s):  
Limit Theorem ◽  
Uniform Distribution ◽  
Real Line ◽  
Symmetric Spaces ◽  
Probability Distributions ◽  
The Real ◽  
Compact Symmetric Spaces

In an article on the philosophy of chance, Poincaré[7] showed that the distribution of the stopping position of a needle pivoted about its centre tends to the uniform distribution on the circle as the distribution of the initial push becomes spread out along the real line. This result was formalized by Feller [2] and strengthened by Mardia [6] as follows.

scholarly journals Exponential Negation of a Probability Distribution

2021 ◽  
Author(s):  
Qinyuan Wu ◽  
Yong Deng ◽  
Neal Xiong
Keyword(s):  
Information Processing ◽  
Probability Distribution ◽  
Uniform Distribution ◽  
Probability Distributions ◽  
Numerical Examples ◽  
Entropy Increase ◽  
Intelligent Information Processing ◽  
Uniform Probability Distribution ◽  
Intelligent Information ◽  
Number Of Iterations

Abstract Negation operation is important in intelligent information processing. Different with existing arithmetic negation, an exponential negation is presented in this paper. The new negation can be seen as a kind of geometry negation. Some basic properties of the proposed negation are investigated, we find that the fix point is the uniform probability distribution. The proposed exponential negation is an entropy increase operation and all the probability distributions will converge to the uniform distribution after multiple negation iterations. The convergence speed of the proposed negation is also faster than the existed negation. The number of iterations of convergence is inversely proportional to the number of elements in the distribution. Some numerical examples are used to illustrate the efficiency of the proposed negation.

scholarly journals Rainfall models – a study over Gangtok

MAUSAM ◽  
2021 ◽  
Vol 61 (2) ◽  
pp. 225-228
Author(s):  
K. SEETHARAM
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Uniform Distribution ◽  
Probability Distribution Function ◽  
Null Hypothesis ◽  
Probability Distributions ◽  
Data Sets ◽  
Type I ◽  
Anderson Darling ◽  
Pearsonian Type

In this paper, the Pearsonian system of curves were fitted to the monthly rainfalls from January to December, in addition to the seasonal as well as annual rainfalls totalling to 14 data sets of the period 1957-2005 with 49 years of duration for the station Gangtok to determine the probability distribution function of these data sets. The study indicated that the monthly rainfall of July and summer monsoon seasonal rainfall did not fit in to any of the Pearsonian system of curves, but the monthly rainfalls of other months and the annual rainfalls of Gangtok station indicated to fit into Pearsonian type-I distribution which in other words is an uniform distribution. Anderson-Darling test was applied to for null hypothesis. The test indicated the acceptance of null-hypothesis. The statistics of the data sets and their probability distributions are discussed in this paper.

Neutrosophic Perspective of Neutrosophic Probability Distributions and its Application

2021 ◽  
pp. 96-109
Author(s):  
M. Lathamaheswari ◽  
◽  
◽  
◽  
◽  
...  
Keyword(s):  
Stochastic Process ◽  
Uniform Distribution ◽  
Binomial Distribution ◽  
Probability Distributions ◽  
Statistical Distributions ◽  
Classical Probability ◽  
Numerical Examples ◽  
Limiting Case ◽  
First Time

Neutrosophical probability is concerned with inequitable and defective topics and processes. This is a subset of Neutrosophic measures that includes a prediction of an event (as opposed to indeterminacy) as well as a prediction of some unpredictability. When there is no such thing as a non-stochastic occurrence, the Neutrosophic probability is the probability of determining a stochastic process. It is a generalisation of classical probability, which states that the probability of correctly predicting an occurrence is zero. Until now, neutrosophic probability distributions have been derived directly from conventional statistical distributions, with fewer contributions to the determination of the for statistical distribution. We introduced the Poission distribution as a limiting case of the Binomial distribution for the first time in this study, and we also proposed Neutrosophic Exponential Distribution and Uniform Distribution for the first time. With numerical examples, the validity and soundness of the proposed notions were also tested.

Distributions of ballot problem random variables

1991 ◽  
Vol 23 (3) ◽  
pp. 586-597 ◽  
Author(s):  
Chern-Ching Chao ◽  
Norman C. Severo
Keyword(s):  
Real Number ◽  
Uniform Distribution ◽  
Positive Real Number ◽  
Probability Distributions ◽  
Sufficient Conditions ◽  
Positive Real ◽  
Discrete Uniform Distribution ◽  
Ballot Problem ◽  
Discrete Uniform ◽  
Necessary And Sufficient

Suppose that in a ballot candidateAscoresavotes and candidateBscoresbvotes, and that all the possible voting records are equally probable. Corresponding to the firstrvotes, letαrandβrbe the numbers of votes registered forAandB, respectively. Let p be an arbitrary positive real number. Denote byδ(a, b, p)[δ*(a,b,ρ)] the number of values ofrfor which the inequality,r =1, ···,a+b, holds. Heretofore the probability distributions of δand δ* have been derived for only a restricted set of values ofa, b, andρ, although, as pointed out here, they are obtainable for all values of (a,b,ρ) by using a result of Takács (1964). In this paper we present a derivation of the distribution ofδ[δ*] whose development, for any (a, b, ρ), leads to both necessary and sufficient conditions forδ[δ*] to have a discrete uniform distribution.

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