Hypergeometric Distribution

Normal approximations to discrete unimodal distributions

Journal of Applied Probability ◽

10.1017/s0021900200115931 ◽

1986 ◽

Vol 23 (04) ◽

pp. 1013-1018

Author(s):

B. G. Quinn ◽

H. L. MacGillivray

Keyword(s):

Stationary Distribution ◽

Sufficient Conditions ◽

Random Variables ◽

Hypergeometric Distribution ◽

Death Process ◽

Normal Approximations ◽

Discrete Random Variables ◽

Birth Death

Sufficient conditions are presented for the limiting normality of sequences of discrete random variables possessing unimodal distributions. The conditions are applied to obtain normal approximations directly for the hypergeometric distribution and the stationary distribution of a special birth-death process.

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Estimating COVID-19 cases infected with the variant alpha (VOC 202012/01): an analysis of screening data in Tokyo, January-March 2021

Theoretical Biology and Medical Modelling ◽

10.1186/s12976-021-00146-x ◽

2021 ◽

Vol 18 (1) ◽

Author(s):

Hiroaki Murayama ◽

Taishi Kayano ◽

Hiroshi Nishiura

Keyword(s):

Confidence Interval ◽

Growth Model ◽

Exponential Growth ◽

Reproduction Number ◽

Hypergeometric Distribution ◽

Actual Number ◽

Growth Data ◽

Exponential Growth Model

Abstract Background In Japan, a part of confirmed patients’ samples have been screened for the variant of concern (VOC), including the variant alpha with N501Y mutation. The present study aimed to estimate the actual number of cases with variant alpha and reconstruct the epidemiological dynamics. Methods The number of cases with variant alpha out of all PCR confirmed cases was estimated, employing a hypergeometric distribution. An exponential growth model was fitted to the growth data of variant alpha cases over fourteen weeks in Tokyo. Results The weekly incidence with variant alpha from 18–24 January 2021 was estimated at 4.2 (95% confidence interval (CI): 0.7, 44.0) cases. The expected incidence in early May ranged from 420–1120 cases per week, and the reproduction number of variant alpha was on the order of 1.5 even under the restriction of contact from January-March, 2021, Tokyo. Conclusions The variant alpha was predicted to swiftly dominate COVID-19 cases in Tokyo, and this has actually occurred by May 2021. Devising the proposed method, any country or location can interpret the virological sampling data.

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APPLICATIONS OF TWO NON-CENTRAL HYPERGEOMETRIC DISTRIBUTIONS OF BIASED SAMPLING STATISTICAL MODELS

FUDMA Journal of Sciences ◽

10.33003/fjs-2020-0404-498 ◽

2021 ◽

Vol 4 (4) ◽

pp. 415-424

Author(s):

A. A. Issa ◽

K. O. Adetunji ◽

T. Alanamu ◽

E. J. Adefila ◽

K. A. Muhammed

Keyword(s):

Statistical Models ◽

Research Work ◽

Hypergeometric Distribution ◽

Biased Sampling ◽

Inversion Method ◽

Urn Model ◽

Fisher Distribution ◽

Direct Inversion ◽

Mean And Variance ◽

Hypergeometric Distributions

Statistical models of biased sampling of two non-central hypergeometric distributions Wallenius' and Fisher's distribution has been extensively used in the literature, however, not many of the logic of hypergeometric distribution have been investigated by different techniques. This research work examined the procedure of the two non-central hypergeometric distributions and investigates the statistical properties which includes the mean and variance that were obtained. The parameters of the distribution were estimated using the direct inversion method of hyper simulation of biased urn model in the environment of R statistical software, with varying odd ratios (w) and group sizes (mi). It was discovered that the two non - central hypergeometric are approximately equal in mean, variance and coefficient of variation and differ as odds ratios (w) becomes higher and differ from the central hypergeometric distribution with ω = 1. Furthermore, in univariate situation we observed that Fisher distribution at (ω = 0.2, 0.5, 0.7, 0.9) is more consistent than Wallenius distribution, although central hypergeometric is more consistent than any of them. Also, in multinomial situation, it was observed that Fisher distribution is more consistent at (ω = 0.2, 0.5), Wallenius distribution at (ω = 0.7, 0.9) and central hypergeometric at (ω = 0.2)

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