Darna Distribution: Properties and Application

Authors

  • Amer Ibrahim Al-Omari Department of Mathematics, Al al-Bayt University
  • Doaa Shraa Al al-Bayt University Faculty of Sciences Department of Mathematics P.O.Box 130095, Mafraq 25113, Jordan

DOI:

https://doi.org/10.1285/i20705948v12n2p520

Keywords:

Mixture distribution, Variance, Bonferroni curve, Stress-Strength reliability, Lorenz curve, Gini index, R´enyi entropy, Stochastic ordering, Reliability analysis

Abstract

In this paper, Darna distribution (DD) is suggested as a new continuousprobability density function. The statistical properties of the DD as the moments,shapes of the distribution, measures of skewness, kurtosis, coefficientof variation are presented as well as some calculations are provided. Also,the maximum likelihood estimators, the Bonferroni and Lorenz curves, andGini Index are obtained. The Stress - Strength Reliability, R´enyi entropy,mean and median deviations are derived and proved. The distribution oforder statistics are presented. The reliability analysis including hazard, reliability,odds, and reverse hazard functions are presented. An application ofWheaton River data is considered.

Author Biography

Amer Ibrahim Al-Omari, Department of Mathematics, Al al-Bayt University

Al al-Bayt University

Faculty of Sciences

Department of Mathematics

P.O.Box 130095, Mafraq 25113,

Jordan

References

Al-Omari, A.I., Alhyasat, K.M., Ibrahim, K. And Abu Baker, M.A. (2019). Power

length-biased Suja distribution: Properties and application. Electronic Journal of Applied

Statistical Analysis, Accepted.

Al-Omari, A., Al-khazaleh, A., and Al-khazaleh, M. (2019). Exponentiated new

Weibull-Pareto distribution. Revista Investigacion Operacional, 40(2):165175.

Al-Omari, A., Al-Nasser, A., and Ciavolino, E. (2019). A size-biased Ishita distribution:

application to real data. Quality and Quantity, 53(1):493512.

Al-Omari, A. and Alsmairan, I. (2019). Length-biased Suja distribution and its applications.

Journal of Applied Probability and Statistics, Accepted.

Al-Omari, A. and Gharaibeh, M. (2018). Topp-Leone Mukherjee-Islam distribution:

properties and applications. Pakistan Journal of Statistics, 34(6):479494.

Adnan, M. (2009). Some Laplace mixture distribution. Journal of Applied Science,

(4): 549-560.

Balakrishnan, N. and Mohanty, N.C. (1972). On the identifiability of finite mixture

of Laguerre distributions. IEEE Trans. Inform. Theory, 18: 514-515.

Bodhisuwan, W., Nanuwong, N. and Pudprommarat, C. (2016). Parameter estimation

for the length biased beta-Pareto distribution and application. Walailak Journal, 13(5):

-315.

Choulakian, V., and Stephens, M.A. (2001). Goodness-of-fit for the generalized Pareto

distribution. Technometrics, 43 (4): 478-484.

Cruz-Medina, I.R. and Hettmansperger, T.P. (2004). Nonparametric estimation in

semi-parametric univariate mixture models. Journal of Statistical Computation and

Simulation, 74: 513-524.

Daniyal, M. and Aleem, M. (2014). On the mixture of Burr and Weibull distributions.

Journal of Statistics Applications and Probability, 3(2): 251-267.

Jiang, R., Zuo, M.J., and Li, H. (1999). Weibull and Inverse Weibull mixture models

allowing negative weights. Reliability. Engineering. System and Safety, 66: 227-234.

Electronic Journal of Applied Statistical Analysis 21

Kamaruzzaman, Z.A., Isa, Z. and Ismail, T.H. (2012). Mixtures of normal distributions:

application to bursa Malaysia Stock Market indices. World Applied Sciences

Journal, 16(16): 781-790.

Hall, P. and Zhou, X. (2003). Nonparametric estimation of component distribution in

a multivariate mixture. The Annals of Statistics, 31: 201-224.

Roy, M.R., Rahman, S. and Ali, M.M. (1992). A class of passion mixture distribution.

Journal of Information and Optimization Sciences, 13: 207-208.

Roy, M.K. and Sinha, S.K. (1995). Negative binomial mixture of normal moment

distribution. Metron, 3: 83-92.

Sultan, S.K. (2007. Mixture of two inverse Weibull distributions: properties and

estimation. Computational Statistics and Data Analysis, 51(11): 5377-5387.

Shanker, R. (2017). Akshaya distribution and its application. American Journal of

Mathematics and Statistics, 7(2): 51-59.

Shanker, R. and Ghebretsadik , A.H. (2013). A new Quasi Lindley distribution.

International Journal of Statistics and System, 8(2): 143-156.

Nareeat, N., Winai, B. and Chookait, P. (2015). A new mixture Pareto distribution

and its application. Thailand Statistician,13(2): 191-207.

Zamanzade, E., and Mahdizadeh, M. (2017). Entropy estimation from ranked set

samples with application to test of fit. Revista Colombiana de Estadstica, Vol. 40(2),

-241.

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Published

14-10-2019

Issue

Vol. 12 No. 2 (2019): Electronic Journal of Applied Statistical Analysis

Section

Original Paper

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