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Displaced Poisson Distribution
In statistics, the displaced Poisson, also known as the hyper-Poisson distribution, is a generalization of the Poisson distribution. The probability mass function is : P(X=n) = \begin e^\dfrac\cdot\dfrac, \quad n=0,1,2,\ldots &\text r\geq 0\\0pt e^\dfrac\cdot\dfrac,\quad n=s,s+1,s+2,\ldots &\text \end where \lambda>0 and ''r'' is a new parameter; the Poisson distribution is recovered at ''r'' = 0. Here I\left(r,\lambda\right) is the Pearson's incomplete gamma function In mathematics, the upper and lower incomplete gamma functions are types of special functions which arise as solutions to various mathematical problems such as certain integrals. Their respective names stem from their integral definitions, which ...: : I(r,\lambda)=\sum^\infty_\frac, where ''s'' is the integral part of ''r''. The motivation given by Staff is that the ratio of successive probabilities in the Poisson distribution (that is P(X=n)/P(X=n-1)) is given by \lambda/n for n>0 and the d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German language, German: ''wikt:Statistik#German, Statistik'', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of statistical survey, surveys and experimental design, experiments.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey sample (statistics), samples. Representative sampling as ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
