A Two Parameter New Distribution for Life Time Data

Arun Kumar Chaudhary; Vijay Kumar

doi:https://doi.org/10.14445/22315373/IJMTT-V66I12P515

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 12 | Year 2020 | Article Id. IJMTT-V66I12P515 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I12P515

A Two Parameter New Distribution for Life Time Data

Arun Kumar Chaudhary, Vijay Kumar

Citation :

Arun Kumar Chaudhary, Vijay Kumar, "A Two Parameter New Distribution for Life Time Data," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 12, pp. 106-115, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I12P515

Abstract

Here in this study we have introduced a two-parameter new distribution. We have discussed some mathematical and statistical characteristics of the distribution such as the probability density function, cumulative distribution function and hazard rate function, survival function, quantile function, the skewness, and kurtosis measures. The model parameters of the proposed distribution are estimated using three well-accepted estimation techniques which are least-square estimation (LSE), maximum likelihood estimation (MLE), and Cramer-Von-Mises estimation (CVME) methods. of The proposed distribution's goodness of fit is also evaluated by fitting it in comparison with some other existing distributions using a real data set.

Keywords

CVM, Estimation, Hazard function, LSE, Survival function

References

[1] Gupta, R. D. and Kundu, D. (1999). Generalized exponential distributions. Australian and New Zealand Journal of Statistics, 41(2), 173 - 188.
[2] Keller, A. Z., Kamath, A. R. R., & Perera, U. D. (1982). Reliability analysis of CNC machine tools. Reliability engineering, 3(6), 449-473.
[3] Joshi, R. K. & Kumar, V. (2020). Lindley exponential power distribution with Properties and Applications. International Journal for Research in Applied Science & Engineering Technology (IJRASET), 8(10), 22-30.
[4] Joshi, R. K. & Kumar, V. (2020). Lindley inverse Weibull distribution: Theory and Applications. Bull. Math. & Stat. Res., 8(3), 32-46.
[5] Joshi, R. K., Sapkota, L.P. & Kumar, V. (2020). The Logistic-Exponential Power Distribution with Statistical Properties and Applications, International Journal of Emerging Technologies and Innovative Research, 7(12), 629-641, ISSN:2349-5162, :http://www.jetir.org/papers/JETIR2012079.pdf
[6] Kumar, V. and Ligges, U. (2011). reliaR: A package for some probability distributions, http://cran.r-project.org/web/packages/reliaR/index.html.
[7] Lai, C., Xie, M., Murthy, D. (2003). A modified weibull distribution. IEEE Trans Reliab 52, 33-37.
[8] Lindley, D. V. (1958). Fiducial Distributions and Bayes Theorem. Journal of the Royal Society, Series B 20, 102-107.
[9] Marshall, A. W. and Olkin, I. (2007). Life Distributions: Structure of Nonparametric, Semiparametric and Parametric Families, Springer, New York.
[10] Moors, J. J. A. (1988). A quantile alternative for kurtosis. Journal of the Royal Statistical Society: Series D (The Statistician), 37(1), 25-32.
[11] Mudholkar G, Srivastava D, & Friemer M (1995). The exponentiated Weibull family: a reanalysis of the bus-motor-failure data. Technometrics 37, 436-445.
[12] Murthy, D.N.P., Xie, M. and Jiang, R. (2003). Weibull Models, Wiley, New York
[13] Nelson, W., & Doganaksoy, N. (1995). Statistical analysis of life or strength data from specimens of various sizes using the power-(log) normal model. Recent Advances in Life-Testing and Reliability, 377-408.
[14] Pham, H., & Lai, C. D. (2007). On recent generalizations of the Weibull distribution. IEEE transactions on reliability, 56(3), 454-458.
[15] R Core Team (2020). R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R-project.org/.
[16] Rinne, H. (2009). The Weibull distribution: a handbook CRC Press. Boca Raton.
[17] Schmuller, J. (2017). Statistical Analysis with R For Dummies, John Wiley & Sons, Inc., New Jersey
[18] Smith, R.M. and Bain, L.J. (1975). An exponential power life-test distribution, Communications in Statistics, 4, 469-481.
[19] Srivastava, A. K., & Kumar, V. (2011). Analysis of software reliability data using exponential power model. IJACSA Editorial.
[20] Swain, J. J., Venkatraman, S. & Wilson, J. R. (1988). Least-squares estimation of distribution functions in johnson’s translation system. Journal of Statistical Computation and Simulation, 29(4), 271–297.
[21] Weibull, W. (1951) A statistical distribution of wide applicability. J Appl Mech 18, 29-37.