ARTICLE
ABSTRACT
A study on two-parameter power Ishita distribution (PID), of which Ishita distribution introduced by Shanker and Shukla (2017 a) is a special case, has been carried out and its important statistical properties including shapes of the density, moments, skewness and kurtosis measures, hazard rate function, and stochastic ordering have been discussed. The maximum likelihood estimation has been discussed for estimating its parameters. An application of the distribution has been explained with a real lifetime data from engineering, and its goodness of fit shows better fit over two-parameter power Akash distribution (PAD), twoparameter power Lindley distribution (PLD) and one-parameter Ishita, Akash, Lindley and exponential distributions.
KEYWORDS
Ishita distribution, moments, hazard rate function, stochastic ordering, maximum likelihood estimation, goodness of fit.
REFERENCES
BADER, M. G., PRIEST, A. M., (1982). Statistical aspects of fiber and bundle strength in hybrid composites, In: Hayashi, T., Kawata, K., Umekawa, S.,(Eds.), Progress in Science in engineering Composites, ICCM-IV, Tokyo, pp. 1129–1136.
GHITANY, M. E., ATIEH, B., NADARAJAH, S., (2008). Lindley distribution and its Application, Mathematics Computing and Simulation, 78, pp. 493–506.
GHITANY, M. E ., Al-MMUTAIRI, D. K., BALAKRISHANAN, N., Al-ENEZI, L. J., (2013). Power Lindley distribution and Associated Inference, Computational Statistics and Data Analysis, 64, pp. 20–33.
LINDLEY, D. V., (1958). Fiducial distributions and Bayes’ Theorem, Journal of the Royal Statistical Society, Series B, 20, pp.102–107.
SHAKED, M., SHANTHIKUMAR, J. G., (1994). Stochastic Orders and Their Applications, Academic Press, New York.
SHANKER, R., (2015). Akash Distribution and Its Applications, International Journal of Probability and Statistics, 4 (3), pp. 65–75.
SHANKER, R., HAGOS, F., SUJATHA, S., (2016). On Modeling of Lifetime Data using One-Parameter Akash, Lindley and Exponential Distributions, Biometrics & Biostatistics International Journal, 3 (2), pp. 1–10.
SHANKER, R., (2017). The Discrete Poisson-Akash Distribution, International Journal of Probability and Statistics, 6 (1), pp. 1–10
SHANKER, R., SHUKLA, K. K., (2017a). Ishita Distribution and its Applications, Biometrics & Biostatistics International Journal, 5 (2), pp. 1–9.
SHANKER, R., SHUKLA, K. K., (2017b). Power Akash distribution and its Application, to appear in Journal of Applied Quantitative Methods.
SHUKLA, K. K., SHANKER, R., (2017). The Discrete Poisson-Ishita Distribution, Communicated.
STACY, E. W., (1962). A generalization of the gamma distribution, Annals of Mathematical Statistics, 33, pp. 1187–1192
