Romanovsky Distribution


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The name “Romanovsky distribution” has been used as another name for the negative hypergeometric distribution [1]. It is also used to describe a restricted occupancy distribution in “ball and urn” investigations [2].

Historical Notes on the Romanovsky Distribution

Haight [3] lists Romanovsky’s distribution in the index yet points to as a sparse entry titled “Romanovsky’s generalization”:

The references point to Biometrika, where “Romanovsky’s generalised curve” is mentioned in [4] as a generalization of Pearson Frequency curves. Specifically, the curve is written as the equation

Where

Where

  • A0, A1, A2, … are constants
  • μ 0, μ1, μ2, …are certain definite one-valued functions of x.

The first term in the series represents one of the Pearson frequency curves depending on the choice of function.

Wishart reports that Romanovsky’s curve “do not appear to better the existing types, owing to the expansion in terms of functions which are not suite to the purpose.” In addition, he notes that apart from a tiny region the series expansions are not convergent and “hence cannot give us really satisfactory fits.”

References

[1] Yusupova A.K., Gafforov R.A. Refining One Theorem For The Romanovsky Distribution. The American Journal of Interdisciplinary Innovations and Research. Vol. 3 No. 06 (2021)
[2] Charalambides, Ch. A. On Restricted and Pseudo-Contagious Occupancy Distributions. Journal of Applied Probability. Vol. 20, No. 4 (Dec., 1983), pp. 872-876 (5 pages)

Published by: Applied Probability Trust.

[3] Haight, F. (1958). Index to the Distributions of Mathematical Statistics. National Bureau of Standards Report.

[4] Wishart, J. On Romanovsky’s Generalised Frequency Curves. Biometrika

Vol. 18, No. 1/2 (Jul., 1926), pp. 221-228 (8 pages)

Published By: Oxford University Press

[5] Romanovsky, V. On the Moments of the Hypergeometrical Series. Biometrika. Vol. 17, No. 1/2 (Jun., 1925), pp. 57-60 (4 pages). Published by: Oxford University Press on behalf of Biometrika Trust