Research Article

A note on the "saturation" of poisson-exponential cumulative function in Hausdorff sense

Volume: 1 Number: 1 September 30, 2018
EN

A note on the "saturation" of poisson-exponential cumulative function in Hausdorff sense

Abstract

In this paper we study the important ''saturation'' characteristic for the Poisson--exponential cumulative distribution function in the Hausdorff sense. The results have independent significance in the study of issues related to lifetime analysis, insurance mathematics, biochemical kinetics, population dynamics and debugging theory. Numerical examples, illustrating our results are presented using programming environment Mathematica.

Keywords

Hausdorff distance,Poisson--exponential cumulative distribution function (Pcdf),Upper and lower bounds

References

  1. [1] V. Cancho, F. Louzada and G. Barriga, The Poisson–exponential lifetime distribution, Comp. Stat. Data Anal., vol. 55, pp. 677–686, 2011.
  2. [2] G. Rodrigues, F. Louzada and P. Ramos, Poisson–exponential distribution: different methods of estimation, J. of Appl. Stat., vol. 45 (1), pp. 128–144, 2018.
  3. [3] F. Louzada, P. Ramos and P. Ferreira, Exponential–Poisson distribution: estimation and applications to rainfall and aircraft data with zero occurrence, Communication in Statistics–Simulation and Computation, 2018.
  4. [4] F. Hausdorff, Set Theory (2 ed.) (Chelsea Publ., New York, (1962 [1957]) (Republished by AMS-Chelsea 2005), ISBN: 978–0–821–83835–8.
  5. [5] N. Pavlov, A. Iliev, A. Rahnev and N. Kyurkchiev, Some software reliability models: Approximation and modeling aspects, LAP LAMBERT Academic Publishing, 2018, ISBN: 978-613-9-82805-0.
  6. [6] N. Pavlov, A. Iliev, A. Rahnev and N. Kyurkchiev, Nontrivial Models in Debugging Theory (Part 2), LAP LAMBERT Academic Publishing, 2018, ISBN: 978-613-9-87794-2.
  7. [7] M. Ramos, A. Percontini, G. Cordeiro and R. Silva, The Burr XII Negative Binomial Distribution with applications to Lifetime Data, Int. J. of Stat. and Prob., vol. 4 (1), pp. 109–124, 2015.
  8. [8] N. Kyurkchiev and S. Markov, Sigmoid functions: Some Approximation and Modelling Aspects. (LAP LAMBERT Academic Publishing, Saarbrucken, 2015); ISBN 978-3-659-76045-7.
  9. [9] N. Kyurkchiev and S. Markov, On the Hausdorff distance between the Heaviside step function and Verhulst logistic function. J. Math. Chem., vol. 54 (1), pp. 109–119, DOI:10.1007/S10910-015-0552-0.
  10. [10] A. Iliev, N. Kyurkchiev and S. Markov, On the Approximation of the step function by some sigmoid functions, Mathematics and Computers in Simulation, 2015, DOI:10.1016/j.matcom.2015.11.005.
APA
Iliev, A., & Kyurkchiev, N. (2018). A note on the "saturation" of poisson-exponential cumulative function in Hausdorff sense. Communications in Advanced Mathematical Sciences, 1(1), 39-44. https://doi.org/10.33434/cams.444785
AMA
1.Iliev A, Kyurkchiev N. A note on the "saturation" of poisson-exponential cumulative function in Hausdorff sense. Communications in Advanced Mathematical Sciences. 2018;1(1):39-44. doi:10.33434/cams.444785
Chicago
Iliev, Anton, and Nikolay Kyurkchiev. 2018. “A Note on the ‘saturation’ of Poisson-Exponential Cumulative Function in Hausdorff Sense”. Communications in Advanced Mathematical Sciences 1 (1): 39-44. https://doi.org/10.33434/cams.444785.
EndNote
Iliev A, Kyurkchiev N (September 1, 2018) A note on the "saturation" of poisson-exponential cumulative function in Hausdorff sense. Communications in Advanced Mathematical Sciences 1 1 39–44.
IEEE
[1]A. Iliev and N. Kyurkchiev, “A note on the ‘saturation’ of poisson-exponential cumulative function in Hausdorff sense”, Communications in Advanced Mathematical Sciences, vol. 1, no. 1, pp. 39–44, Sept. 2018, doi: 10.33434/cams.444785.
ISNAD
Iliev, Anton - Kyurkchiev, Nikolay. “A Note on the ‘saturation’ of Poisson-Exponential Cumulative Function in Hausdorff Sense”. Communications in Advanced Mathematical Sciences 1/1 (September 1, 2018): 39-44. https://doi.org/10.33434/cams.444785.
JAMA
1.Iliev A, Kyurkchiev N. A note on the "saturation" of poisson-exponential cumulative function in Hausdorff sense. Communications in Advanced Mathematical Sciences. 2018;1:39–44.
MLA
Iliev, Anton, and Nikolay Kyurkchiev. “A Note on the ‘saturation’ of Poisson-Exponential Cumulative Function in Hausdorff Sense”. Communications in Advanced Mathematical Sciences, vol. 1, no. 1, Sept. 2018, pp. 39-44, doi:10.33434/cams.444785.
Vancouver
1.Anton Iliev, Nikolay Kyurkchiev. A note on the "saturation" of poisson-exponential cumulative function in Hausdorff sense. Communications in Advanced Mathematical Sciences. 2018 Sep. 1;1(1):39-44. doi:10.33434/cams.444785