A characterization of the binomial and negative binomial distribution by regression of products

Metrika ◽  
1993 ◽  
Vol 40 (1) ◽  
pp. 237-242 ◽  
Author(s):  
Jerzy Pusz
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial

scholarly journals KAJIAN VARIANCE MEAN RATIO PADA SIMULASI SEBARAN DATA BINOMIAL NEGATIF

2020 ◽  
Vol 4 (4) ◽  
pp. 615-626
Author(s):  
Choirun Nisa ◽  
Muhammad Nur Aidi ◽  
I Made Sumertajaya
Keyword(s):  
Data Collection ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Data Distribution ◽  
P Value ◽  
Binomial Data ◽  
Simulation Data ◽  
Count Distribution

The negative binomial distribution is one of the data collection counts that focuses on success and failure events. This study conducted a study of the distribution of negative binomial data to determine the characterization of the distribution based on the value of Variance Mean Ratio (VMR). Simulation data are generated based on negative binomial distribution with a combination of p and n parameters. The results of the VMR study on negative binomial distribution simulation data show that the VMR value will be smaller when the p-value is large and the VMR value is more stable as the sample size increases. Simulation data of negative binomial distribution when p≥0.5 begins to change data distribution to the distribution of Poisson and binomial. The calculation VMR value can be used as a reference for detecting patterns of data count distribution.

A characterization of the gamma distribution by the negative binomial distribution

1980 ◽  
Vol 17 (04) ◽  
pp. 1138-1144 ◽  
Author(s):  
Jan Engel ◽  
Mynt Zijlstra
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Gamma Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Random Variable ◽  
One To One

It is proved that for a Poisson process there exists a one-to-one relation between the distribution of the random variable N(Y) and the distribution of the non-negative random variable Y. This relation is used to characterize the gamma distribution by the negative binomial distribution. Furthermore it is applied to obtain some characterizations of the exponential distribution.

scholarly journals On a Characterization of Zero-Inflated Negative Binomial Distribution

2015 ◽  
Vol 05 (06) ◽  
pp. 511-513
Author(s):  
R. Suresh ◽  
G. Nanjundan ◽  
S. Nagesh ◽  
Sadiq Pasha
Keyword(s):  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial

A characterization of the gamma distribution by the negative binomial distribution

1980 ◽  
Vol 17 (4) ◽  
pp. 1138-1144 ◽  
Author(s):  
Jan Engel ◽  
Mynt Zijlstra
Keyword(s):  
Poisson Process ◽  
Exponential Distribution ◽  
Gamma Distribution ◽  
Negative Binomial Distribution ◽  
Binomial Distribution ◽  
Negative Binomial ◽  
Random Variable ◽  
One To One

It is proved that for a Poisson process there exists a one-to-one relation between the distribution of the random variable N(Y) and the distribution of the non-negative random variable Y. This relation is used to characterize the gamma distribution by the negative binomial distribution. Furthermore it is applied to obtain some characterizations of the exponential distribution.

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.

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