scholarly journals A New Neutrosophic Negative Binomial Distribution: Properties and Applications

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Rehan Ahmad Khan Sherwani ◽  
Sadia Iqbal ◽  
Shumaila Abbas ◽  
Muhammad Aslam ◽  
Ali Hussein AL-Marshadi
Keyword(s):  
Probability Distribution ◽  
Order Statistics ◽  
Generating Function ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Hazard Rate ◽  
Negative Binomial ◽  
Real Life ◽  
Probability Generating Function ◽  
Interval Valued

Many problems in real life exist that are full of confusion, vagueness, and ambiguity. The quantification of such issues in a scientific way is the need of time. The negative binomial distribution is an important discrete probability distribution from the account of classical probability distribution theory. The distribution was used to study the chance of kth success in n trials before n − 1 failures for crisp data. The literature lacks in dealing with the situations for interval-valued data under negative binomial distribution. In this research, the neutrosophic negative binomial distribution is proposed to generalize the classical negative binomial distribution. The generalized proposed distribution considers the indeterminacy and crisp form from interval-valued. Several properties of the proposed distribution, such as moment generating function, characteristic function, and probability generating function, are also derived. Furthermore, the derivation of reliability analysis properties such as survival, hazard rate, reversed hazard rate, cumulative hazard rate, mills ratio, and odds ratio are also presented. In addition, order statistics for the proposed distribution, including w th , joint, median, minimum, and maximum order statistics are part of the paper. The proposed distribution is discussed from the real data applications perspective by considering the different case studies. This research opens the way to deal with the problems that follow conventional conveyances and include nonprecisely determined details simultaneously.

scholarly journals A Note on the Net Premium for a Generalized Largest Claims Reinsurance Cover

1998 ◽  
Vol 28 (1) ◽  
pp. 153-162 ◽  
Author(s):  
Raoul M. Berglund
Keyword(s):  
Order Statistics ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Mutually Independent

AbstractIn the present paper the author gives net premium formulae for a generalized largest claims reinsurance cover. If the claim sizes are mutually independent and identically 3-parametric Pareto distributed and the number of claims has a Poisson, binomial or negative binomial distribution, formulae are given from which numerical values can easily be obtained. The results are based on identities for compounded order statistics.

scholarly journals A mechanistic model for the negative binomial distribution of single-cell mRNA counts

2019 ◽  
Author(s):  
Lisa Amrhein ◽  
Kumar Harsha ◽  
Christiane Fuchs
Keyword(s):  
Steady State ◽  
Probability Distribution ◽  
Single Cell ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Probability Distributions ◽  
Mechanistic Model ◽  
Steady State Probability ◽  
Degradation Models

SummarySeveral tools analyze the outcome of single-cell RNA-seq experiments, and they often assume a probability distribution for the observed sequencing counts. It is an open question of which is the most appropriate discrete distribution, not only in terms of model estimation, but also regarding interpretability, complexity and biological plausibility of inherent assumptions. To address the question of interpretability, we investigate mechanistic transcription and degradation models underlying commonly used discrete probability distributions. Known bottom-up approaches infer steady-state probability distributions such as Poisson or Poisson-beta distributions from different underlying transcription-degradation models. By turning this procedure upside down, we show how to infer a corresponding biological model from a given probability distribution, here the negative binomial distribution. Realistic mechanistic models underlying this distributional assumption are unknown so far. Our results indicate that the negative binomial distribution arises as steady-state distribution from a mechanistic model that produces mRNA molecules in bursts. We empirically show that it provides a convenient trade-off between computational complexity and biological simplicity.Graphical Abstract

The Lindley negative-binomial distribution: Properties, estimation and applications to lifetime data

2020 ◽  
Vol 70 (4) ◽  
pp. 917-934
Author(s):  
Muhammad Mansoor ◽  
Muhammad Hussain Tahir ◽  
Gauss M. Cordeiro ◽  
Sajid Ali ◽  
Ayman Alzaatreh
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Hazard Rate ◽  
Negative Binomial ◽  
Real Data ◽  
Moment Generating Function ◽  
Estimation Methods ◽  
Model Parameters ◽  
Proposed Model ◽  
Rate Functions

AbstractA generalization of the Lindley distribution namely, Lindley negative-binomial distribution, is introduced. The Lindley and the exponentiated Lindley distributions are considered as sub-models of the proposed distribution. The proposed model has flexible density and hazard rate functions. The density function can be decreasing, right-skewed, left-skewed and approximately symmetric. The hazard rate function possesses various shapes including increasing, decreasing and bathtub. Furthermore, the survival and hazard rate functions have closed form representations which make this model tractable for censored data analysis. Some general properties of the proposed model are studied such as ordinary and incomplete moments, moment generating function, mean deviations, Lorenz and Bonferroni curve. The maximum likelihood and the Bayesian estimation methods are utilized to estimate the model parameters. In addition, a small simulation study is conducted in order to evaluate the performance of the estimation methods. Two real data sets are used to illustrate the applicability of the proposed model.

scholarly journals The alpha power Teissier distribution and its applications

2021 ◽  
Vol 16 (2) ◽  
pp. 2733-2747
Author(s):  
Joseph Thomas Eghwerido
Keyword(s):  
Data Analysis ◽  
Generating Function ◽  
Hazard Rate ◽  
Real Life ◽  
Probability Generating Function ◽  
Moment Generating Function ◽  
Rate Function ◽  
Alpha Power ◽  
Real Life Data ◽  
Proposed Model

Statistical distribution that represents the true characteristics of real-life data is paramount to data analysis. Thus, this study introduces a tractable alpha power Teissier distribution (APOT). Some statistical properties of the proposed model like moments, probability generating function, moment generating function and order statistic were examined. The shape of the hazard rate and survival functions were investigated. The shapes of the hazard rate function indicated increasing, decreasing, J-shaped and bathtub shapes. The results of the data analysis indicated that the APOT model performed better when compared to some existing classical statistical distributions.

Niche Sharing in Intertidal Mollusks and Decapods in Rocky Shore of Easter Island

2019 ◽  
Vol 53 (5) ◽  
pp. 417-422
Author(s):  
P. De los Ríos ◽  
E. Ibáñez Arancibia
Keyword(s):  
Spatial Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Rocky Shore ◽  
Negative Binomial ◽  
Null Model ◽  
Easter Island ◽  
Published Data ◽  
Distribution Analysis ◽  
Field Works

Abstract The coastal marine ecosystems in Easter Island have been poorly studied, and the main studies were isolated species records based on scientific expeditions. The aim of the present study is to apply a spatial distribution analysis and niche sharing null model in published data on intertidal marine gastropods and decapods in rocky shore in Easter Island based in field works in 2010, and published information from CIMAR cruiser in 2004. The field data revealed the presence of decapods Planes minutus (Linnaeus, 1758) and Leptograpsus variegatus (Fabricius, 1793), whereas it was observed the gastropods Nodilittorina pyramidalis pascua Rosewater, 1970 and Nerita morio (G. B. Sowerby I., 1833). The available information revealed the presence of more species in data collected in 2004 in comparison to data collected in 2010, with one species markedly dominant in comparison to the other species. The spatial distribution of species reported in field works revealed that P. minutus and N. morio have aggregated pattern and negative binomial distribution, L. variegatus had uniform pattern with binomial distribution, and finally N. pyramidalis pascua, in spite of aggregated distribution pattern, had not negative binomial distribution. Finally, the results of null model revealed that the species reported did not share ecological niche due to competition absence. The results would agree with other similar information about littoral and sub-littoral fauna for Easter Island.

ANALISIS RISIKO OPERASIONAL MENGGUNAKAN PENDEKATAN DISTRIBUSI KERUGIAN DENGAN METODE AGREGAT

2011 ◽  
Vol 10 (2) ◽  
pp. 1
Author(s):  
Y. ARBI ◽  
R. BUDIARTI ◽  
I G. P. PURNABA
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Financial Institution ◽  
Expected Value ◽  
Insurance Companies ◽  
Limited Data ◽  
Loss Distribution Approach ◽  
Potential Loss ◽  
The Impact

Operational risk is defined as the risk of loss resulting from inadequate or failed internal processes or external problems. Insurance companies as financial institution that also faced at risk. Recording of operating losses in insurance companies, were not properly conducted so that the impact on the limited data for operational losses. In this work, the data of operational loss observed from the payment of the claim. In general, the number of insurance claims can be modelled using the Poisson distribution, where the expected value of the claims is similar with variance, while the negative binomial distribution, the expected value was bound to be less than the variance.Analysis tools are used in the measurement of the potential loss is the loss distribution approach with the aggregate method. In the aggregate method, loss data grouped in a frequency distribution and severity distribution. After doing 10.000 times simulation are resulted total loss of claim value, which is total from individual claim every simulation. Then from the result was set the value of potential loss (OpVar) at a certain level confidence.

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