International Journal of Data Envelopment Analysis and *Operations Research*
ISSN (Print): ISSN Pending ISSN (Online): ISSN Pending Website: http://www.sciepub.com/journal/ijdeaor Editor-in-chief: Ehsan Zanboori
Open Access
Journal Browser
Go
International Journal of Data Envelopment Analysis and *Operations Research*. 2016, 2(1), 7-15
DOI: 10.12691/ijdeaor-2-1-2
Open AccessArticle

On The Continuous Poisson Distribution

Salah H Abid1, and Sajad H Mohammed1

1Mathematics Department, Education College, Al-Mustansiriya University, Baghdad, Iraq

Pub. Date: August 15, 2016

Cite this paper:
Salah H Abid and Sajad H Mohammed. On The Continuous Poisson Distribution. International Journal of Data Envelopment Analysis and *Operations Research*. 2016; 2(1):7-15. doi: 10.12691/ijdeaor-2-1-2

Abstract

There are no scientific works deal directly and Extensively with the continuous Poisson distribution (CPD). There are some of rare allusions here and there. In this paper we will take this issue on our responsibility. We consider here the continuous Poisson distribution. Different methods to estimate CPD parameters are studied, Maximum Likelihood estimator, Moments estimator, Percentile estimator, least square estimator and weighted least square estimator. An empirical study is conducted to compare among these methods performances. We also consider the generating issue. Other empirical experiments are conducted to build a model for bandwidth parameter which is used for Poisson density estimation.

Keywords:
Continuous Poisson distribution MLE Percentile estimator bandwidth selection density estimation AR(1) model

Creative CommonsThis work is licensed under a Creative Commons Attribution 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

References:

[1]  Abramowitz, M. and Stegun, I. (1970). “Handbook of Mathematical Functions: with Formulas, Graphs, and Mathematical Tables”, 9-Revised edition, Dover Publications, USA.
 
[2]  Alissandrakis, C., Dialets, D. and Tsiropoula, G. (1987) “Determination of the mean lifetime of solar features from photographic observations”, Astronomy and Astrophysics journal , vol. 174, no. 1-2, March, p. 275-280.
 
[3]  Bowman, A. (1984). “An alternative method of cross-validation for the smoothing of density estimates”; Biometrika, 71; 353-360.
 
[4]  Bowman, A. and Azzalini, A. (1997). “Applied Smoothing Techniques for Data Analysis: The Kernel Approach with S-Plus Illustrations”; Oxford Univ. Press.
 
[5]  Deheuvels, P. (1977). “Estimation nonparamétrique de la densité par histogrammesgeneralizes”; Rev. Statist. Appl. 25 5-42.
 
[6]  Epanechnikov, V.A. (1969). “Non-parametric estimation of a multivariate probability density”. Theory of Probability and its Applications 14: 153-158.
 
[7]  Faraway, J. and Jhun, M. (1990). “Bootstrap choice of bandwidth for density estimation”, J. Amer. Statist. Assoc. 85 (1990) 1119-1122.
 
[8]  Haight, F. (1967) “Handbook of the Poisson Distribution”; 1st Edition, Wiley, USA.
 
[9]  Herzog, A., Binder, T. , Friedl, F., Jahne, B. and Kostina, A. (2010). “Estimating water-sided vertical gas concentration profiles by inverse modeling” ; International Conference on Engineering Optimization, September 6-9, Lisbon, Portugal.
 
[10]  Ilienko, A. and Klesov, O. (2013). “Continuous counterparts of Poisson and binomial distributions and their properties”; Annals Univ. Sci. Budapest., Sect. Comp. 39 (2013) 137-147.
 
[11]  Kao J (1959). A graphical estimation of mixed Weibull parameters in life testing electron tubes., Technometrics, 1, 389-407.
 
[12]  Kingman, J. (1993). “Poisson Processes”, 1st Edition, Oxford Studies in Probability (Book 3), Clarendon Press, UK.
 
[13]  Mann N, Schafer R and Singpurwalla N (1974). Methods for Statistical Analysis of Reliability and Life Data., New York, Wiley.
 
[14]  Scott, D. (1979). “On optimal and data-based histograms”; Biometrika; 66; 605-610.
 
[15]  Scott, D. and Terrell, G. (1987). “Biased and unbiased cross-validation in density estimation”; J. Amer. Statist. Assoc.; 82; 1131-1146.
 
[16]  Sheather, S. and Jones, M. (1991). “A reliable data-based bandwidth selection method for kernel density estimation”; J. Roy. Statist. Soc. Ser.B 53, 683-690.
 
[17]  Sheather, S. (2004). “Density Estimation”; Statistical Science, 19(4), pp. 588-597.
 
[18]  Silverman, B. (1986). “Density Estimation for Statistics and Data Analysis”; Chapman and Hall, London.
 
[19]  Simonoff, J. (1996). “Smoothing Methods in Statistics”; Springer, New York.
 
[20]  Swain J, Venkatraman S and Wilson J (1988). Least squares estimation of distribution function in Johnson's translation system, Journal of Statistical Computation and Simulation, 29, 271-297.
 
[21]  Turowski, J. (2010). “Probability distributions of bed load transport rates: A new derivation and comparison with field data”; water resources research, Volume 46, Issue 8.
 
[22]  Venables, W. and Ripley, B. (2002). “Modern Applied Statistics with S”, 4th ed. Springer, New York.
 
[23]  Wand, M. and Jones, M. (1995). “Kernel Smoothing”; London: Chapman & Hall/CRC.
 
[24]  Webb, G. (2000). “MultiBoosting: A Technique for Combining Boosting and Wagging”, Machine Learning, 40, 159-39.