The distribution of the sum of independent and non identically generalized Lindley random variables

References

• Abd El-Monsef, M. 2016. A new Lindley distribution with location parameter. Communications in Statistics - Theory and Methods 45:5204–19. doi:10.1080/03610926.2014.941496.
   Web of Science ®Google Scholar
• Alouini, M., A. Abdi, and M. Kaveh. 2001. Sum of gamma variates and performance of wireless communication systems over Nakagami-fading channels. IEEE Transactions on Vehicular Technology 50 (6):1471–80. doi:10.1109/25.966578.
   Web of Science ®Google Scholar
• Amari, S., and R. Misra. 1997. Closed-form expressions for distribution of sum of exponential random variables. IEEE Transactions on Reliability 46 (4):519–22. doi:10.1109/24.693785.
   Web of Science ®Google Scholar
• Bradley, D., and C. Gupta. 2002. On the distribution of the sum of n non-identically distributed uniform random variables. Annals of the Institute of Statistical Mathematics 54 (3):689–700. doi:10.1023/A:1022483715767.
   Web of Science ®Google Scholar
• Daniels, H. 1954. Saddlepoint approximations in statistics. The Annals of Mathematical Statistics 25 (4):631–50. doi:10.1214/aoms/1177728652.
   Google Scholar
• Ding, C. 1992. Algorithm AS 275: Computing the non-central χ2 distribution function. Journal of the Royal Statistical Society, Series C 41:478–82.
   Web of Science ®Google Scholar
• Duchesne, P., and P. De Micheaux. 2010. Computing the distribution of quadratic forms: Further comparisons between the Liu-Tang-Zhang approximation and exact methods. Computational Statistics & Data Analysis 54 (4):858–62. doi:10.1016/j.csda.2009.11.025.
   Web of Science ®Google Scholar
• Eisinga, R., M. Grotenhuis, and B. Pelzer. 2013. Saddlepoint approximation for the sum of independent non-identically distributed binomial random variables. Statistica Neerlandica 67 (2):190–201. doi:10.1111/stan.12002.
   Web of Science ®Google Scholar
• Farebrother, R. 1987. Algorithm AS 231: The distribution of a noncentral χ2 variable with nonnegative degrees of freedom. Journal of the Royal Statistical Society, Series C 17:402–405.
   Google Scholar
• Gabler, S., and C. Wolff. 1987. A quick and easy approximation to the distribution of a sum of weighted chi-square variables. Statistische Hefte 28 (1):317–25. doi:10.1007/BF02932611.
   Google Scholar
• Ghitany, M., B. Atieh, and S. Nadarajah. 2008. Lindley distribution and its application. Mathematics and Computers in Simulation 78 (4):493–506. doi:10.1016/j.matcom.2007.06.007.
   Web of Science ®Google Scholar
• Gómez, Y., H. Bolfarine, and H. Gómez. 2014. A new extension of the exponential distribution. Revista Colombiana de Estadística 37 (1):25–34. doi:10.15446/rce.v37n1.44355.
   Google Scholar
• Kamps, U. 1990. Characterizations of the exponential distribution by weighted sums of iid random variables. Statistical Papers 31 (1):233–37. doi:10.1007/BF02924695.
   Google Scholar
• Khuong, H., and H. Y. Kong. 2006. General expression for pdf of a sum of independent exponential random variables. IEEE Communications Letters 10:159–61.
   Web of Science ®Google Scholar
• Kitani, M., and H. Murakami. 2020. On the distribution of the sum of the independent and non-identically extended exponential random variables. Japanese Journal of Statistics and Data Science 3 (1):23–37. doi:10.1007/s42081-019-00046-y.
   Google Scholar
• Lindley, D. 1958. Fiducial distributions and Bayes’ theorem. Journal of the Royal Statistical Society: Series B (Methodological) 20 (1):102–107. doi:10.1111/j.2517-6161.1958.tb00278.x.
   Web of Science ®Google Scholar
• Lugannani, R., and S. Rice. 1980. Saddlepoint approximation for the distribution of the sum of independent random variables. Advances in Applied Probability 12 (2):475–90. doi:10.2307/1426607.
   Web of Science ®Google Scholar
• Mathai, A. 1982. Storage capacity of a dam with gamma type inputs. Annals of the Institute of Statistical Mathematics 34 (3):591–97. doi:10.1007/BF02481056.
   Web of Science ®Google Scholar
• Miyazaki, R., and H. Murakami. 2020. The non-null limiting distribution of the generalized Baumgartner statistic based on the Fourier series approximation. Statistical Papers 61 (5):1893–909. doi:10.1007/s00362-018-1012-2.
   Web of Science ®Google Scholar
• Moschopoulos, P. 1985. The distribution of the sum of independent gamma random variables. Annals of the Institute of Statistical Mathematics 37 (3):541–44. doi:10.1007/BF02481123.
   Web of Science ®Google Scholar
• Murakami, H. 2014. A saddlepoint approximation to the distribution of the sum of independent non-identically uniform random variables. Statistica Neerlandica 68 (4):267–75. doi:10.1111/stan.12032.
   Web of Science ®Google Scholar
• Murakami, H. 2015. Approximations to the distribution of sum of independent non-identically gamma random variables. Mathematical Sciences 9 (4):205–13. doi:10.1007/s40096-015-0169-2.
   Web of Science ®Google Scholar
• Nadarajah, S. 2008. A review of results on sums of random variables. Acta Applicandae Mathematicae 103 (2):131–40. doi:10.1007/s10440-008-9224-4.
   Web of Science ®Google Scholar
• Nadarajah, S., X. Jiang, and J. Chu. 2015. A saddlepoint approximation to the distribution of the sum of independent non-identically beta random variables. Statistica Neerlandica 69 (2):102–14. doi:10.1111/stan.12051.
   Web of Science ®Google Scholar
• Olds, E. 1952. A note on the convolution of uniform distributions. The Annals of Mathematical Statistics 23 (2):282–85. doi:10.1214/aoms/1177729446.
   Google Scholar
• Penev, S., and T. Raykov. 2000. A wiener germ approximation of the noncentral chi square distribution and of its quantiles. Computational Statistics 15 (2):219–28. doi:10.1007/s001800000029.
   Web of Science ®Google Scholar
• Potuschak, H., and W. Müller. 2009. More on the distribution of the sum of uniform random variables. Statistical Papers 50 (1):177–83. doi:10.1007/s00362-007-0050-y.
   Web of Science ®Google Scholar
• Sadooghi-Alvandi, S., A. Nematollahi, and R. Habibi. 2009. On the distribution of the sum of independent uniform random variables. Statistical Papers 50 (1):171–75. doi:10.1007/s00362-007-0049-4.
   Web of Science ®Google Scholar
• Shanker, R., and A. Mishra. 2013. A quasi Lindley distribution. African Journal of Mathematics and Computer Science Research 6:64–71.
   Google Scholar
• Shanker, R., S. Sharma, and R. Shanker. 2013. A two-parameter Lindley distribution for modeling waiting and survival times data. Applied Mathematics 04 (02):363–68. doi:10.4236/am.2013.42056.
   Google Scholar
• Solomon, H., and M. Stephens. 1977. Distribution of a sum of weighted chi-square variables. Journal of the American Statistical Association 72 (360):881–85. doi:10.2307/2286480.
   Web of Science ®Google Scholar
• Tank, F., and S. Eryilmaz. 2015. The distributions of sum, minima and maxima of generalized geometric random variables. Statistical Papers 56 (4):1191–203. doi:10.1007/s00362-014-0632-4.
   Web of Science ®Google Scholar
• Zakerzadeh, H., and A. Dolati. 2009. Generalized Lindley distribution. Journal of Mathematical Extension 3:13–25.
   Google Scholar