A New Probability Model for Hydrologic Events: Properties and Applications

  • Tassaddaq Hussain
  • Hassan S. Bakouch
  • Zafar Iqbal


Upon the motivation of unstable climatic conditions of the world like excess of rains, drought and huge floods, we introduce a versatile hydrologic probability model with two scale parameters. The proposed model contains Lindley and exponentiated exponential (Lindley in J R Stat Soc Ser B 20:102–107, 1958; Gupta and Kundu in Biom J 43(1):117–130, 2001) distributions as special cases. Various properties of the distribution are obtained, such as shapes of the density and hazard functions, moments, mean deviation, information-generating function, conditional moments, Shannon entropy, L-moments, order statistics, information matrix and characterization via hazard function. Parameters are estimated via maximum likelihood estimation method. A simulation scheme is provided for generating the random data from the proposed distribution. Four data sets are used for comparing the proposed model with a set of well-known hydrologic models, such as generalized Pareto, log normal (3), log Pearson type III, Kappa(3), Gumbel, generalized logistic and generalized Lindley distributions, using some goodness-of-fit tests. These comparisons render the proposed model suitable and representative for hydrologic data sets with least loss of information attitude and a realistic return period, which render it as an appropriate alternate of the existing hydrologic models. Supplementary materials for this paper are available online.


Probability distributions Information-generating function Maximum likelihood estimator Return level Rainfall data 



Authors would like to thank the two anonymous referees for their constructive comments and suggestions that greatly improved this manuscript. Authors also are grateful to Muhammad Nauman Khan for his help on editing the Latex template.

Supplementary material

13253_2017_313_MOESM1_ESM.pdf (210 kb)
Supplementary material 1 (pdf 210 KB)


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Copyright information

© International Biometric Society 2017

Authors and Affiliations

  • Tassaddaq Hussain
    • 1
  • Hassan S. Bakouch
    • 2
  • Zafar Iqbal
    • 3
  1. 1.Department of Mathematics, Faculty of ScienceMirpur University of Science and TechnologyMirpurPakistan
  2. 2.Department of Mathematics, Faculty of ScienceTanta UniversityTantaEgypt
  3. 3.Department of StatisticsGovernment Post Graduate CollegeSatellite Town, GujranwalaPakistan

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