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8 - Singh System of Frequency Distributions

Published online by Cambridge University Press:  06 November 2020

Vijay P. Singh  and
Lan Zhang
Vijay P. Singh
Affiliation:
Texas A & M University
Lan Zhang
Affiliation:
Texas A & M University
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Summary

There are many frequency distributions whose cumulative distribution functions (CDFs) cannot be expressed in closed form. Examples of such distributions are normal, lognormal, gamma, Pearson type III, among others. If a distribution has a closed form CDF then its probability density function (PDF) can be easily obtained by differentiation but vice versa is not tractable. Using certain hypotheses on the relation between PDF and CDF based on empirical data, the CDFs of a large number of distributions can be derived. This chapter discusses the derivation of CDFs of such distributions many of which are frequently used in hydrologic, hydraulic, environmental, and water resources engineering.

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Systems of Frequency Distributions for Water and Environmental Engineering , pp. 194 - 206
Publisher: Cambridge University Press
Print publication year: 2020

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References

Burr, I. W. (1942). Cumulative frequency functions. Annals of Mathematical Statistics 13, pp. 215‒232.CrossRefGoogle Scholar
Singh, V. P. (2018). System of frequency distributions for water and environmental engineering, Physica A 506, pp. 50‒74. doi: 10.1016/j.physa.2018.03.038.CrossRefGoogle Scholar
Stoppa, G. (1990). A new generating system of income distribution models. Quarderni di Statistica e Mathematica Applicata alle Science Economico-Sociali 12, pp. 47‒55.Google Scholar
Stoppa, G. (1993). Una tavola per modeli di probabilita. Metron 51, pp. 99‒117.Google Scholar

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