Likelihood Based Estimation of the Parameters of a Log-Linear Nonhomogeneous Poisson Process
International Journal of Science and Research (IJSR)

International Journal of Science and Research (IJSR)
www.ijsr.net | Open Access | Fully Refereed | Peer Reviewed International Journal

ISSN: 2319-7064



Downloads: 127 | Weekly Hits: ⮙3 | Monthly Hits: ⮙14

Research Paper | Statistics | Kenya | Volume 3 Issue 9, September 2014

Likelihood Based Estimation of the Parameters of a Log-Linear Nonhomogeneous Poisson Process

Kariuki Veronica, Luke Akongo Orawo, Ali Salim Islam

Non-homogeneous Poisson process (NHPP) has widely been used over decades to model random processes that are time dependent (e.g. occurrences of serious road accidents). After the times of occurrence of a particular event have been observed, the problem of estimating the intensity function arises. In this paper, we consider maximum likelihood estimation of the parameters of a NHPP with log-linear intensity function. The maximum likelihood estimates of the unknown parameters of the intensity function are obtained numerically and the confidence intervals and regions are constructed from the respective graphs of the maximized and joint relative likelihood functions. We present simulation results which demonstrate the good performance of our confidence intervals and regions as compared to those based on large sample approaches. The large sample confidence intervals may be inaccurate in the sense that they exclude plausible parameter values and include values that are very implausible. Our approach is optimal for small sample inferences on the parameters of a log-linear NHPP.

Keywords: Nonhomogeneous Poisson process, log-linear, relative likelihood function, estimation, intensity function

Edition: Volume 3 Issue 9, September 2014

Pages: 200 - 204

Share this Article

How to Cite this Article?

Kariuki Veronica, Luke Akongo Orawo, Ali Salim Islam, "Likelihood Based Estimation of the Parameters of a Log-Linear Nonhomogeneous Poisson Process", International Journal of Science and Research (IJSR), https://www.ijsr.net/search_index_results_paperid.php?id=SEP1420, Volume 3 Issue 9, September 2014, 200 - 204

Enter Your Registered Email Address





Similar Articles with Keyword 'log-linear'

Downloads: 108 | Weekly Hits: ⮙6

Research Paper, Statistics, India, Volume 9 Issue 7, July 2020

Pages: 451 - 457

Estimation of COVID-19 Prevalence under Closed Population using Capture-Recapture Approach

Rakesh Kumar, R.S.Mishra

Share this Article

Downloads: 127 | Weekly Hits: ⮙3 | Monthly Hits: ⮙14

Research Paper, Statistics, Kenya, Volume 3 Issue 9, September 2014

Pages: 200 - 204

Likelihood Based Estimation of the Parameters of a Log-Linear Nonhomogeneous Poisson Process

Kariuki Veronica, Luke Akongo Orawo, Ali Salim Islam

Share this Article

Downloads: 261 | Weekly Hits: ⮙5 | Monthly Hits: ⮙17

Research Paper, Statistics, Nepal, Volume 3 Issue 6, June 2014

Pages: 161 - 166

Accelerated Failure Time Models: An Application in the Survival of Acute Liver Failure Patients in India

Shankar Prasad Khanal, V. Sreenivas, Subrat K. Acharya

Share this Article

Similar Articles with Keyword 'estimation'

Downloads: 34

Research Paper, Statistics, Kenya, Volume 4 Issue 9, September 2015

Pages: 1216 - 1224

Spatial Temporal Modelling of Tuberculosis in Kenya Using Small Area Estimation

Kipruto H; Mung?atu J; Ogila K; Adem A; Mwalili S; Kibuchi E; Ong'ang'o JR; Sang G

Share this Article

Downloads: 49 | Weekly Hits: ⮙1 | Monthly Hits: ⮙7

Research Paper, Statistics, India, Volume 9 Issue 12, December 2020

Pages: 1603 - 1610

Poisson Inverse NHE Distribution with Theory and Applications

Arun Kumar Chaudhary, Vijay Kumar

Share this Article

Downloads: 59

Research Paper, Statistics, Kenya, Volume 7 Issue 6, June 2018

Pages: 121 - 126

Modelling Extreme Maximum Rainfall Using Generalized Extreme Value Distribution: Case Study Kigali City

Uwimana Oliver; Joseph K. Mung'atu

Share this Article

Downloads: 90

Research Paper, Statistics, India, Volume 5 Issue 8, August 2016

Pages: 1599 - 1604

Poisson-Gamma Counting Process as a Survival Model under Size-Biased Sampling

Pawan Kumar Srivastava, R. S. Srivastava

Share this Article

Downloads: 93 | Weekly Hits: ⮙5 | Monthly Hits: ⮙12

Survey Paper, Statistics, India, Volume 3 Issue 11, November 2014

Pages: 1296 - 1298

Lower Bounds on Variance of Estimators Past, Present and Future

A. Shanubhogue, D. B. Jadhav

Share this Article

Similar Articles with Keyword 'intensity function'

Downloads: 123 | Weekly Hits: ⮙1 | Monthly Hits: ⮙11

M.Tech / M.E / PhD Thesis, Statistics, Tanzania, Volume 5 Issue 10, October 2016

Pages: 1858 - 1868

Non Homogeneous Poisson Process Modelling of Seasonal Extreme Rainfall Events in Tanzania

Triphonia Ngailo, Nyimvua Shaban, Joachim Reuder, Edwin Rutalebwa, Isaac Mugume

Share this Article

Downloads: 127 | Weekly Hits: ⮙3 | Monthly Hits: ⮙14

Research Paper, Statistics, Kenya, Volume 3 Issue 9, September 2014

Pages: 200 - 204

Likelihood Based Estimation of the Parameters of a Log-Linear Nonhomogeneous Poisson Process

Kariuki Veronica, Luke Akongo Orawo, Ali Salim Islam

Share this Article



Top