Power Size Biased Two-Parameter Akash Distribution

Khaldoon  Alhyasat; Ibrahim  Kamarulzaman; Amer Ibrahim  Al-Omari; Mohd Aftar Abu Bakar

doi:DOI 10.21307/stattrans-2020-045

Power Size Biased Two-Parameter Akash Distribution

Khaldoon Alhyasat School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia , Ibrahim Kamarulzaman School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia , Amer Ibrahim Al-Omari School of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Malaysia ORCID:https://orcid.org/0000-0002-6901-8263 , Mohd Aftar Abu Bakar Department of Mathematics, Faculty of Science, Al al-Bayt University, Mafraq, Jordan ORCID:https://orcid.org/0000-0002-3009-6168 Statistics in Transition new series, vol. 21, 2020, 3, pages: 73-91 Published online: 4 September 2020 DOI DOI 10.21307/stattrans-2020-045

860 Views 43 Downloads

ARTICLE

(English) PDF

ABSTRACT

In this paper, the two-parameter Akash distribution is generalized to size-biased twoparameter Akash distribution (SBTPAD). A further modification to SBTPAD is introduced, creating the power size-biased two-parameter Akash distribution (PSBTPAD). Several statistical properties of PSBTPAD distribution are proved. These properties include the following: moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, the maximum likelihood estimation of the distribution parameters, and finally order statistics. Moreover, plots of the density and distribution functions of PSBTPAD are presented and a reliability analysis is considered. The Rényi entropy of PSBTPAD is proved and the application of real data is discussed.

KEYWORDS

Akash distribution, two-parameter Akash distribution, size-biased distribution, moments, coefficient of variation, coefficient of skewness, coefficient of kurtosis, maximum likelihood estimation, entropy

REFERENCES

ABEBE, B., SHANKER , R., (2018). A discrete Akash distribution with applications. Turkiye Klinikleri J Biostat, 10(1), p. 1012.

AL-OMARI, A. I., ALHYASAT, K. M., IBRAHIM, K., ABU BAKER, M. A., (2019). Power length-biased Suja distribution: Properties and application. Electronic Journal of Applied Statistical Analysis, Vol. 12(2), pp. 429–452.

AL-OMARI, A. I. AL-NASSER, A. D., CIAVOLINO, E., (2019). A size-biased Ishita distribution application to real data. Quality and Quantity, Vol. 53(1), pp. 493–512.

AL-OMARI, A. I., ALSMAIRAN, I. K., (2019). Length-biased Suja distribution: Properties and application. Journal of Applied Probability and Statistics, Vol. 14(3), pp. 95–116.

AL-OMARI, A.I., ZAMANZADE, E., (2017). Goodness-of-fit tests for Laplace distribution in ranked set sampling. Revista Investigacin Operacional, Vol. 38(4), pp. 366–276.

Al-OMARI, A. I., ZAMANZADE, E., (2018). Goodness of fit tests for logistic distribution based on Phi-divergence. Electronic Journal of Applied Statistical Analysis, Vol. 11(1), pp. 185–195.

AL-OMARI, A.I., HAQ, A., (2019). Novel entropy estimators of a continuous random variable. International Journal of Modeling, Simulation, and Scientific Computing, Vol. 10(2), 1950004.

FISHER, R. A., (1934). The effects of methods of ascertainment upon the estimation of frequencies. Ann. Eugen, Vol. 6, pp. 13–25.

FULLER, J.R., E.R., FRIEMAN, S.W., QUINN, J. B. QUINN, G. D. and CARTER, W. C., (1994). Fracture mechanics approach to the design of glass aircraft windows: A case study. SPIE Proc., 2286, pp. 419–430.

GEORGEA, D., GEORGEA, S., (2013). Marshall–Olkin Esscher transformed Laplace distribution and processes. Brazilian Journal of Probability and Statistics, 27(2), pp. 162–184.

GHITANY, M. E., AL-MMUTAIRI, D. K., BALAKRISHANAN, N., AL-ENEZI, L. J., (2013). Power Lindley distribution and Associated Inference. Comput. Stat. Data Anal., Vol. 64, pp. 20–33.

GUPTA, R. C., KEATING, J. P., (1986). Relations for reliability measures under length biased sampling. Scand. J. Stat, Vol. 13, pp. 49–56.

GUPTA, R. C., KIRMANI, S. N., (1990). The role of weighted distributions in stochastic modeling. Commun. Stat. - Theory Methods, Vol. 19, pp. 3147–3162.

HAQ, M. A., USMAN, R. M., HASHMI, S. and AL-OMARI, A. I., (2017). The Marshall- Olkin length-biased exponential distribution and its applications. JKSUS, Vol. 31(2), pp. 246–251.

OLUYEDE, B. O., (1999). On inequalities and selection of experiments for lengthbiased distributions. Probab. Eng. Inf. Sci. Vol. 13(2), pp. 169–185.

PATIL, G. P., RAO, G. R., (1978). Weighted distributions and size biased sampling with applications to wildlife populations and human families. Biometrics, Vol. 34, pp. 179–189.

RAO, R., (1965). On discrete distributions arising out of methods of ascertainment. Sankhya. Series A. Vol. 27(2), pp. 311–324.

SAGHIR, A., HAMEDANI, G.G. TAZEEM, S. and KHADIM, A., (2017). Weighted distributions: A brief review, perspective and characterizations, IJSP, Vol. 6(3), pp. 109–131.

SHANKER, R., (2015). Akash distribution and its applications. International Journal of Probability and Statistics, 4 (3), pp. 65–75.

SHANKER, R., (2016). A Quasi Akash distribution and its applications. ASR, 30(1), pp. 135–160.

SHANKER, R., (2017). Size-biased Poisson-Akash distribution and its applications. International Journal of Statistics and Applications, 7(6), pp. 289–297.

SHANKER, R., (2017). Suja distribution and its application. Int J Probab Stat, Vol. 6(2), pp. 11–19.

SHANKER, R., FESSHAYE, H. and TESFAZGHI, T., (2016). On Poisson-Akash distribution and its applications. Biometrics & Biostatistics International Journal, 3(6), pp. 1–9.

SHANKER, R., SHUKLA, K. K., (2017). On two-parameter Akash distribution. BBIJ, Vol. 6(5), pp. 1–11.

SHANKER, R., SHUKLA, K. K., and LEONIDA, T. A., (2017). A two-parameter Poisson-Akash distribution with properties and applications. International Journal of Probability and Statistics, 7(4), pp. 114–123.

SHANKER, R., SHUKLA, K. K., SHANKR, R. and PRATAB, A., (2018). A generalized Akash distribution. Biometrics & Biostatistics International Journal, 7(1), pp. 18?26.

SHANKER, R., SHUKLA, K.K., (2017). Power Akash Distribution and Its Application. Journal of Applied Quantitative Methods, 12(3), pp. 1–10.

SHUKLA, K. K., SHANKER, R., (2018). Power Ishita distribution and its application to model lifetime data. Statistics in Transition New Series, Vol. 19(1), pp. 135–148.

ZAMANZADE, E., MAHDIZADEH, M., (2017). Entropy estimation from ranked set samples with application to test of fit. Revista Colombiana de Estadstica, Vol. 40(2), pp. 223–241.

ZAMANZADE, E., (2014). Testing uniformity based on new entropy estimators, Journal of Statistical Computation and Simulation, Vol. 85(16), pp. 3191–3205.

ZAMANZADE, E., ARGHAMI, N. R., (2011). Goodness-of-fit test based on correcting moments of modified entropy estimator. Journal of Statistical Computation and Simulation, Vol. 81(12), pp. 2077–2093.