Logistic Inverse Exponential Distribution
with Properties and Applications

Arun Kumar Chaudhary; Vijay KumaR

doi:https://doi.org/10.14445/22315373/IJMTT-V66I10P518

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 66 | Issue 10 | Year 2020 | Article Id. IJMTT-V66I10P518 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I10P518

Logistic Inverse Exponential Distribution with Properties and Applications

Arun Kumar Chaudhary, Vijay KumaR

Citation :

Arun Kumar Chaudhary, Vijay KumaR, "Logistic Inverse Exponential Distribution with Properties and Applications," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 10, pp. 151-162, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I10P518

Abstract

In this study, we have introduced a two-parameter univariate continuous distribution called Logistic inverse exponential distribution. Some mathematical and statistical properties of the distribution such as the shapes of the probability density, cumulative distribution and hazard rate functions, survival function, quantile function, the skewness, and kurtosis measures are derived and established. To estimate the model parameters, we have employed three well-known estimation methods namely maximum likelihood estimation (MLE), least-square estimation (LSE), and Cramer-Von-Mises estimation (CVME) methods. A real data set is considered to explore the applicability and capability of the proposed distribution also AIC, BIC, CAIC and HQIC are calculated to assess the validity of the Logistic inverse exponential distribution.

Keywords

Cramer-Von-Mises estimation, Exponential distribution, Least-square estimation, Logistic distribution,Maximum likelihood estimation.

References

[1] Basheer, A. M. (2019). Marshall–Olkin alpha power inverse exponential distribution: properties and applications. Annals of data science, 1-13.
[2] Birnbaum, Z.W., Saunders, S.C. (1969), "Estimation for a family of life distributions with applications to fatigue", Journal of Applied Probability, vol. 6, 328 -347.
[3] Burr, I.W. (1942). Cumulative frequency distribution, Annals of Mathematical Statistics, 13, 215-232.
[4] Casella, G., & Berger, R. L. (1990). Statistical Inference. Brooks/ Cole Publishing Company, California.
[5] Chaudhary, A. K., Sapkota, L. P. & Kumar, V. (2020). Truncated Cauchy power–inverse exponential distribution: Theory and Applications. IOSR Journal of Mathematics (IOSR-JM), 16(4), 12-23.
[6] Chen, Z. (2000). A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function. Statistics & Probability Letters, 49, 155-161.
[7] Gupta, R. D. and Kundu, D. (1999). Generalized exponential distributions, Australian and New Zealand Journal of Statistics, 41(2), 173 - 188.
[8] Keller, A. Z., Kamath, A. R. R., & Perera, U. D. (1982). Reliability analysis of CNC machine tools. Reliability engineering, 3(6), 449-473.
[9] Kumar, V. and Ligges, U. (2011). reliaR: A package for some probability distributions, http://cran.r-project.org/web/packages/reliaR/index.html.
[10] Lan, Y., & Leemis, L. M. (2008). The logistic–exponential survival distribution. Naval Research Logistics (NRL), 55(3), 252-264.
[11] Ming Hui, E. G. (2019). Learn R for applied statistics. Springer, New York.
[12] Moors, J. J. A. (1988). A quantile alternative for kurtosis. Journal of the Royal Statistical Society: Series D (The Statistician), 37(1), 25-32.
[13] Oguntunde, P. E., Adejumo, A., & Owoloko, E. A. (2017). Application of Kumaraswamy inverse exponential distribution to real lifetime data. International Journal of Applied Mathematics and Statistics.
[14] Prakash, G. (2012). Inverted Exponential distribution under a Bayesian viewpoint. Journal of Modern Applied Statistical Methods, 11(1), 16.
[15] Rao, G. S. (2013). Estimation of reliability in multicomponent stress-strength based on inverse exponential distribution. International Journal of Statistics and Economics, 10(1), 28-37.
[16] 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/
[17] Rizzo, M. L. (2008). Statistical computing with R. Chapman & Hall/CRC.
[18] Smith, R.M. and Bain, L.J. (1975). An exponential power life-test distribution, Communications in Statistics, 4, 469-481
[19] 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.
[20] Tahir, M. H., Cordeiro, G. M., Alzaatreh, A., Mansoor, M., & Zubair, M. (2016). The logistic-X family of distributions and its applications. Communications in Statistics-Theory and Methods, 45(24), 7326-7349.