BibTex RIS Cite

STATISTICAL PROPERTIES AND APPLICATIONS OF A NEW LINDLEY EXPONENTIAL DISTRIBUTION

Year 2016, Volume: 29 Issue: 4, 831 - 838, 19.12.2016

Abstract

This article studied a New Lindley Exponential distribution using the Lindley generalized family of distributions. Expressions for its densities, survival function, hazard function, quantile function and distribution of order statistics were derived. Its sub-models were identified and the New Lindley Exponential distribution was applied to two real life datasets to assess its flexibility over the Lindley distribution and the Exponential distribution. Excerpt from the results indicates that the New Lindley Exponential distribution performed better than both the Lindley distribution and the Exponential distribution based on their log-likelihood and Akaike Information Criteria values.

References

  • Alexander C., Cordeiro, G. M., Ortega, E. M. M., Sarabia, J. M. (2012). Generalized beta generated distributions. Computational Statistics and Data Analysis, 56:1880–1897
  • Alizadeh M., Cordeiro G. M., de Brito E., Demetrio C. G. B. (2015a). The Beta Marshall-Olkin family of distributions. Journal of Statistical Distributions and Applications, 2 (4), 1-18
  • Alizadeh M., Tahir M. H., Cordeiro G. M., Mansoor M., Zubair M., Hamedani G. G. (2015b). The Kumaraswamy Marshal-Olkin family of distributions. Journal of the Egyptian Mathematical Society, 23, 546-557
  • Alqallaf F., Ghitany M. E., Agostinelli C. (2015). Weighted Exponential Distribution: Different Methods of Estimations. Applied Mathematics and Information Sciences, 9 (3), 1167-1173
  • Alzaatreh A., Famoye F., Lee C. (2013). Weibull-Pareto Distribution and Its Applications. Communications in Statistics-Theory and Methods, 42 (9), 1673-1691
  • Alzaatreh, A., Famoye, F., Lee, C. (2014). The gamma-normal distribution: Properties and applications. Computational Statistics and Data Analysis 69:67–80
  • Alzaghal A., Lee C., Famoye F. (2013). Exponentiated T-X family of distributions with some applications. International Journal of Probability and Statistics, 2 (3), 31-49
  • Amini, M., MirMostafaee, S. M. T. K., Ahmadi, J. (2014). Log-gamma-generated families of distributions. Statistics: A Journal of Theoretical and Applied Statistics, 48 (4), 913-932
  • Bhati D., Malik M. A., Vaman H. J. (2014). Lindley-Exponential Distribution: Properties and Applications. Metron, 73 (3), 335-357
  • Bourguignon M., Silva R. B., Cordeiro G. M. (2014). The Weibull-G Family of Probability Distributions. Journal of Data Science, 12, 53-68
  • Cakmakyapan S., Ozel G. (2016). The Lindley Family of Distributions: Properties and Applications. Hacettepe Journal of Mathematics and Statistics, 46, 1-27, doi: 10.15672/hjms.201611615850
  • Cordeiro G. M., de Castro M. (2011). A New family of Generalized Distributions. Journal of Statistical computation and Simulation, 81, 883-898
  • Cordeiro G. M, Ortega E. M., da Cunha D. C. (2013). The Exponentiated Generalized Class of Distributions. Journal of Data Science, 11, 1-27
  • Eugene N., Lee C., Famoye F. (2002). Beta-Normal distribution and Its Applications. Communications in Statistics: Theory and Methods, 31, 497-512
  • Ghitany M. E., Atieh B., Nadarajah S. (2008). Lindley Distribution and Its Application. Mathematics and Computers in Simulation, 78 (4), 493-506
  • Marshall A. W., Olkin I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and weibull families. Biometrika, 84 (3), 641-652
  • Nassar M. M., Nada N. K. (2011). The Beta Generalized Pareto Distribution. Journal of Statistics: Advances in Theory Application, 6 (1): 1-17
  • Oguntunde P. E., Odetunmibi O. A., Adejumo A. O. (2014). A Study of Probability Models in Monitoring Environmental Pollution in Nigeria. Journal of Probability and Statistics, Volume 2014, Article ID: 864965, 6 Pages
  • Oguntunde P. E., Owoloko E. A., Balogun O. S. (2016). On A New Weighted Exponential Distribution: Theory and Application, Asian Journal of Applied Sciences, 9 (1), 1-12
  • Owoloko E. A., Oguntunde P. E., Adejumo A. O. (2015). Performance Rating of the Transmuted Exponential Distribution: An Analytical Approach. SpringerPlus, 4:818, 1-15
  • Risti´c M. M., Balakrishnan N. (2012). The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation 82:1191–1206
  • Shanker R., Fesshaye H., Selvaraj S. (2015). On Modeling of Lifetimes Data Using Exponential and Lindley Distributions. Biometrics & Biostatistics International Journal, 2 (5): 00042. DOI: 10.15406/bbij.2015.02.00042
  • Shanker R. (2016). Aradhana Distribution and Its Applications. International Journal of Statistics and Applications, 6 (1), 23-34.
  • Shaw W., Buckley I. (2007). The alchemy of probability distributions: Beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research Report
  • Tahir M. H., Cordeiro G. M., Alzaatreh A., Mansoor M., Zubair M. (2015). The Logistic-X Family of Distributions and Its Applications. Communication in Statistics-Theory and Methods (To Appear).
  • Torabi H., Montazari N. H. (2012). The gamma-uniform distribution and its application. Kybernetika, 48:16–30
  • Torabi H., Montazari N. H. (2014). The logistic-uniform distribution and its application. Communications in Statistics–Simulation and Computation 43:2551–2569
  • .
Year 2016, Volume: 29 Issue: 4, 831 - 838, 19.12.2016

Abstract

References

  • Alexander C., Cordeiro, G. M., Ortega, E. M. M., Sarabia, J. M. (2012). Generalized beta generated distributions. Computational Statistics and Data Analysis, 56:1880–1897
  • Alizadeh M., Cordeiro G. M., de Brito E., Demetrio C. G. B. (2015a). The Beta Marshall-Olkin family of distributions. Journal of Statistical Distributions and Applications, 2 (4), 1-18
  • Alizadeh M., Tahir M. H., Cordeiro G. M., Mansoor M., Zubair M., Hamedani G. G. (2015b). The Kumaraswamy Marshal-Olkin family of distributions. Journal of the Egyptian Mathematical Society, 23, 546-557
  • Alqallaf F., Ghitany M. E., Agostinelli C. (2015). Weighted Exponential Distribution: Different Methods of Estimations. Applied Mathematics and Information Sciences, 9 (3), 1167-1173
  • Alzaatreh A., Famoye F., Lee C. (2013). Weibull-Pareto Distribution and Its Applications. Communications in Statistics-Theory and Methods, 42 (9), 1673-1691
  • Alzaatreh, A., Famoye, F., Lee, C. (2014). The gamma-normal distribution: Properties and applications. Computational Statistics and Data Analysis 69:67–80
  • Alzaghal A., Lee C., Famoye F. (2013). Exponentiated T-X family of distributions with some applications. International Journal of Probability and Statistics, 2 (3), 31-49
  • Amini, M., MirMostafaee, S. M. T. K., Ahmadi, J. (2014). Log-gamma-generated families of distributions. Statistics: A Journal of Theoretical and Applied Statistics, 48 (4), 913-932
  • Bhati D., Malik M. A., Vaman H. J. (2014). Lindley-Exponential Distribution: Properties and Applications. Metron, 73 (3), 335-357
  • Bourguignon M., Silva R. B., Cordeiro G. M. (2014). The Weibull-G Family of Probability Distributions. Journal of Data Science, 12, 53-68
  • Cakmakyapan S., Ozel G. (2016). The Lindley Family of Distributions: Properties and Applications. Hacettepe Journal of Mathematics and Statistics, 46, 1-27, doi: 10.15672/hjms.201611615850
  • Cordeiro G. M., de Castro M. (2011). A New family of Generalized Distributions. Journal of Statistical computation and Simulation, 81, 883-898
  • Cordeiro G. M, Ortega E. M., da Cunha D. C. (2013). The Exponentiated Generalized Class of Distributions. Journal of Data Science, 11, 1-27
  • Eugene N., Lee C., Famoye F. (2002). Beta-Normal distribution and Its Applications. Communications in Statistics: Theory and Methods, 31, 497-512
  • Ghitany M. E., Atieh B., Nadarajah S. (2008). Lindley Distribution and Its Application. Mathematics and Computers in Simulation, 78 (4), 493-506
  • Marshall A. W., Olkin I. (1997). A new method for adding a parameter to a family of distributions with application to the exponential and weibull families. Biometrika, 84 (3), 641-652
  • Nassar M. M., Nada N. K. (2011). The Beta Generalized Pareto Distribution. Journal of Statistics: Advances in Theory Application, 6 (1): 1-17
  • Oguntunde P. E., Odetunmibi O. A., Adejumo A. O. (2014). A Study of Probability Models in Monitoring Environmental Pollution in Nigeria. Journal of Probability and Statistics, Volume 2014, Article ID: 864965, 6 Pages
  • Oguntunde P. E., Owoloko E. A., Balogun O. S. (2016). On A New Weighted Exponential Distribution: Theory and Application, Asian Journal of Applied Sciences, 9 (1), 1-12
  • Owoloko E. A., Oguntunde P. E., Adejumo A. O. (2015). Performance Rating of the Transmuted Exponential Distribution: An Analytical Approach. SpringerPlus, 4:818, 1-15
  • Risti´c M. M., Balakrishnan N. (2012). The gamma-exponentiated exponential distribution. Journal of Statistical Computation and Simulation 82:1191–1206
  • Shanker R., Fesshaye H., Selvaraj S. (2015). On Modeling of Lifetimes Data Using Exponential and Lindley Distributions. Biometrics & Biostatistics International Journal, 2 (5): 00042. DOI: 10.15406/bbij.2015.02.00042
  • Shanker R. (2016). Aradhana Distribution and Its Applications. International Journal of Statistics and Applications, 6 (1), 23-34.
  • Shaw W., Buckley I. (2007). The alchemy of probability distributions: Beyond Gram-Charlier expansions and a skew-kurtotic-normal distribution from a rank transmutation map. Research Report
  • Tahir M. H., Cordeiro G. M., Alzaatreh A., Mansoor M., Zubair M. (2015). The Logistic-X Family of Distributions and Its Applications. Communication in Statistics-Theory and Methods (To Appear).
  • Torabi H., Montazari N. H. (2012). The gamma-uniform distribution and its application. Kybernetika, 48:16–30
  • Torabi H., Montazari N. H. (2014). The logistic-uniform distribution and its application. Communications in Statistics–Simulation and Computation 43:2551–2569
  • .
There are 28 citations in total.

Details

Journal Section Statistics
Authors

Pelumi Oguntunde

Adebowale Adejumo This is me

Hillary Okagbue

Manoj Rastogi

Publication Date December 19, 2016
Published in Issue Year 2016 Volume: 29 Issue: 4

Cite

APA Oguntunde, P., Adejumo, A., Okagbue, H., Rastogi, M. (2016). STATISTICAL PROPERTIES AND APPLICATIONS OF A NEW LINDLEY EXPONENTIAL DISTRIBUTION. Gazi University Journal of Science, 29(4), 831-838.
AMA Oguntunde P, Adejumo A, Okagbue H, Rastogi M. STATISTICAL PROPERTIES AND APPLICATIONS OF A NEW LINDLEY EXPONENTIAL DISTRIBUTION. Gazi University Journal of Science. December 2016;29(4):831-838.
Chicago Oguntunde, Pelumi, Adebowale Adejumo, Hillary Okagbue, and Manoj Rastogi. “STATISTICAL PROPERTIES AND APPLICATIONS OF A NEW LINDLEY EXPONENTIAL DISTRIBUTION”. Gazi University Journal of Science 29, no. 4 (December 2016): 831-38.
EndNote Oguntunde P, Adejumo A, Okagbue H, Rastogi M (December 1, 2016) STATISTICAL PROPERTIES AND APPLICATIONS OF A NEW LINDLEY EXPONENTIAL DISTRIBUTION. Gazi University Journal of Science 29 4 831–838.
IEEE P. Oguntunde, A. Adejumo, H. Okagbue, and M. Rastogi, “STATISTICAL PROPERTIES AND APPLICATIONS OF A NEW LINDLEY EXPONENTIAL DISTRIBUTION”, Gazi University Journal of Science, vol. 29, no. 4, pp. 831–838, 2016.
ISNAD Oguntunde, Pelumi et al. “STATISTICAL PROPERTIES AND APPLICATIONS OF A NEW LINDLEY EXPONENTIAL DISTRIBUTION”. Gazi University Journal of Science 29/4 (December 2016), 831-838.
JAMA Oguntunde P, Adejumo A, Okagbue H, Rastogi M. STATISTICAL PROPERTIES AND APPLICATIONS OF A NEW LINDLEY EXPONENTIAL DISTRIBUTION. Gazi University Journal of Science. 2016;29:831–838.
MLA Oguntunde, Pelumi et al. “STATISTICAL PROPERTIES AND APPLICATIONS OF A NEW LINDLEY EXPONENTIAL DISTRIBUTION”. Gazi University Journal of Science, vol. 29, no. 4, 2016, pp. 831-8.
Vancouver Oguntunde P, Adejumo A, Okagbue H, Rastogi M. STATISTICAL PROPERTIES AND APPLICATIONS OF A NEW LINDLEY EXPONENTIAL DISTRIBUTION. Gazi University Journal of Science. 2016;29(4):831-8.