scholarly journals Some Notes on the Omega Distribution and the Pliant Probability Distribution Family

Algorithms ◽  
2020 ◽  
Vol 13 (12) ◽  
pp. 324
Author(s):  
Maria T. Vasileva

In 2020 Dombi and Jónás (Acta Polytechnica Hungarica 17:1, 2020) introduced a new four parameter probability distribution which they named the pliant probability distribution family. One of the special members of this family is the so-called omega probability distribution. This paper deals with one of the important characteristic “saturation” of these new cumulative functions to the horizontal asymptote with respect to Hausdorff metric. We obtain upper and lower estimates for the value of the Hausdorff distance. A simple dynamic software module using CAS Mathematica and Wolfram Cloud Open Access is developed. Numerical examples are given to illustrate the applicability of obtained results.

BIOMATH ◽  
2016 ◽  
Vol 5 (2) ◽  
pp. 1609041 ◽  
Author(s):  
Anton Iliev Iliev ◽  
Nikolay Kyurkchiev ◽  
Svetoslav Markov

In this paper we study the one-sided Hausdorff distance between the shifted Heaviside step--function and the transmuted Stannard growth function. Precise upper and lower bounds for the Hausdorff distance have been obtained. We present a software module (intellectual property) within the programming environment CAS Mathematica for the analysis of the growth curves. Numerical examples, illustrating our results are given, too.


Author(s):  
Helena Gaspars-Wieloch

Purpose – scenario planning is very helpful when the decision maker deals with uncertain issues. Probabilities are also frequently applied to such problems. In the paper, we examine the correctness of combining probabilities with scenario planning in economic decisions which are usually made under uncertainty. The goal of the article is to find and discuss cases where the use of probabilities in scenario planning is appropriate and cases where such an approach is not desira-ble. Research methodology – in order to achieve this target, we first make a concise literature review of existing approaches concerning the application of probabilities to scenario planning. Then, we investigate and compare diverse decision mak-ing circumstances presented by means of numerical examples and differing from each other with regard to the nature of the decision problem (way of payoff estimation, novelty degree of the problem, access to historical data etc.) and the de-cision maker’s objectives and preferences (one-shot or multi-shots decisions, attitude towards risk). We explore the newsvendor problem, the spare parts quantity problem, the project selection problem and the project time management with scenario-based decision project graphs. Findings – the work contains both recommendations already described in the literature and suggestions formulated by the author. We get to the point that scenario planning is unquestionable support for decision making under uncertainty, however, the use of probabilities as an accompanying tool may be necessary and justified in some specific cases only. Their significance depends for instance on (1) the number of times a given variant is supposed to be executed; (2) the de-cision maker’s knowledge about the considered problem; (3) the novelty degree of the problem; (4) the decision maker’s conviction that the probability values really reflect his/her attitude towards risk. The analysis of numerical examples leads us to the conclusion that scenario planning should not be linked with the likelihood (1) for one-shot decisions problems; (2) for decision problems related to different kinds of innovation; (3) in the case of lack of certainty which type of proba-bility definition ought to be applied to a given situation; (4) if the decision maker anticipates new future factors not in-cluded in historical data. Research limitations – in the paper we mainly analyse one-criterion problems and payoff matrices with data precisely de-fined. Further conclusions can be obtained after investigating multi-criteria cases and examples with interval payoffs. We limit our research to selected probability definitions. Nevertheless, a wider review can lead to new interesting observa-tions. Practical implications – the aforementioned findings are crucial in such domains as economic modeling and decision the-ory. The results of the research can be used in planning, management, and decision optimization. They provide valuable guidelines for each decision maker dealing with an uncertain future. Originality/Value – authors of previous papers related to this topic have already formulated many significant conclusions. However, this contribution examines the problem from a new point of view since it concentrates on novel decisions, con-cerning unique, innovative or innovation projects (products). It encourages the decision makers to treat problems usually called in the literature “stochastic problems” (i.e. with known probability distribution) as “strategic problems” (i.e. with unknown probability distribution). This is especially the case of the newsvendor problem and the spare parts quantity problem


Author(s):  
Lipeng Pan ◽  
Yong Deng

Dempster-Shafer evidence theory can handle imprecise and unknown information, which has attracted many people. In most cases, the mass function can be translated into the probability, which is useful to expand the applications of the D-S evidence theory. However, how to reasonably transfer the mass function to the probability distribution is still an open issue. Hence, the paper proposed a new probability transform method based on the ordered weighted averaging and entropy difference. The new method calculates weights by ordered weighted averaging, and adds entropy difference as one of the measurement indicators. Then achieved the transformation of the minimum entropy difference by adjusting the parameter r of the weight function. Finally, some numerical examples are given to prove that new method is more reasonable and effective.


2018 ◽  
Vol 2018 ◽  
pp. 1-25
Author(s):  
Weiping Wang ◽  
Meiqi Wang ◽  
Xiong Luo ◽  
Lixiang Li ◽  
Wenbing Zhao

This paper is concerned with the passivity problem of memristive bidirectional associative memory neural networks (MBAMNNs) with probabilistic and mixed time-varying delays. By applying random variables with Bernoulli distribution, the information of probability time-varying delays is taken into account. Furthermore, we consider the probability distribution of the variation and the extent of the delays; therefore, the results derived are less conservative than in the existing papers. In particular, the leakage delays as well as distributed delays are all taken into consideration. Based on appropriate Lyapunov-Krasovskii functionals (LKFs) and some useful inequalities, several conditions for passive performance are established in linear matrix inequalities (LMIs). Finally, numerical examples are given to demonstrate the feasibility of the presented theories, and the results reveal that the probabilistic and mixed time-varying delays have an unstable influence on the system and should not be ignored.


2006 ◽  
Vol 23 (04) ◽  
pp. 497-508 ◽  
Author(s):  
V. S. S. YADAVALLI ◽  
G. ARIVARIGNAN ◽  
N. ANBAZHAGAN

This paper considers a two commodity continuous review inventory system. The demand points for each commodity are assumed to form Poisson processes. It is further assumed that the demand for the first commodity require the one unit of second commodity in addition to the first commodity with probability p1. Similarly, the demand for the second commodity require the one unit of first commodity in addition to the second commodity with probability p2. This assumption model the situation in which a buyer who intends to buy one particular commodity may also go for another commodity. The limiting probability distribution for the joint inventory levels is computed. Various operational characteristics, expression for the long run total expected cost rate is derived. The results are illustrated with numerical examples.


2021 ◽  
Author(s):  
Qinyuan Wu ◽  
Yong Deng ◽  
Neal Xiong

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.


2006 ◽  
Vol 1 (1) ◽  
pp. 12-14
Author(s):  
Jörg Meyer

2019 ◽  
Vol 15 (5) ◽  
pp. 155014771984938 ◽  
Author(s):  
Xiaozhuan Gao ◽  
Yong Deng

Target recognition in uncertain environments is a hot issue. Fusion rules are used to combine the sensor reports from different sources. In this situation, obtaining more information to make correct decision is an essential issue. Probability distribution is one of the most used methods to represent uncertainty information. In addition, the negation of probability distribution provides a new view to represent the uncertainty information. In this article, the existing negation of probability distribution is extended with Tsallis entropy. The main reason is that different systems have different parameter q. Some numerical examples are used to demonstrate the efficiency of the proposed method. Besides, the article also discusses the application of negation in target recognition based on sensor fusion to further demonstrate the importance of negation.


Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1963 ◽  
Author(s):  
Nikolay Kyurkchiev

In this paper, we study some properties of an exponentially optimal filter proposed by Tadmor and Tanner. More precisely, we consider the problem for approximating the function of rectangular type F(t) by the class of exponential functions σadapt(t) about the Hausdorff metric. We prove upper and lower estimates for “saturation”—d (in the case q=2). New activation and “semi-activation” functions based on σadapt(t) are defined. Some related problems are discussed. We also consider modified families of functions with “polynomial variable transfer”. Numerical examples, illustrating our results using CAS MATHEMATICA are given.


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