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Gamma Gompertz Distribution
In probability and statistics, the Gamma/Gompertz distribution is a continuous probability distribution. It has been used as an aggregate-level model of customer lifetime and a model of mortality risks. Specification Probability density function The probability density function of the Gamma/Gompertz distribution is: :f(x;b,s,\beta) = \frac where b > 0 is the scale parameter and \beta, s > 0\,\! are the shape parameters of the Gamma/Gompertz distribution. Cumulative distribution function The cumulative distribution function of the Gamma/Gompertz distribution is: :\beginF(x;b,s,\beta)& = 1 - \frac, x>0, b,s,\beta>0 \\ pt& = 1-e^, \beta=1\\\end Moment generating function The moment generating function is given by: :\begin \text(e^)= \begin\displaystyle \beta^s \frac (s+1,(t/b)+s;(t/b)+s+1;1-\beta), & \beta \ne 1; \\ \displaystyle \frac,& \beta =1. \end \end where (a,b;c;z) = \sum_^\infty a)_k(b)_k/(c)_k^k/k! is a Hypergeometric function. Properties The Gamma/Gompert ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gamma Gompertz Probability Distribution
Gamma (uppercase , lowercase ; ''gámma'') is the third letter of the Greek alphabet. In the system of Greek numerals it has a value of 3. In Ancient Greek, the letter gamma represented a voiced velar stop . In Modern Greek, this letter represents either a voiced velar fricative or a voiced palatal fricative (while /g/ in foreign words is instead commonly transcribed as γκ). In the International Phonetic Alphabet and other modern Latin-alphabet based phonetic notations, it represents the voiced velar fricative. History The Greek letter Gamma Γ is a grapheme derived from the Phoenician letter (''gīml'') which was rotated from the right-to-left script of Canaanite to accommodate the Greek language's writing system of left-to-right. The Canaanite grapheme represented the /g/ phoneme in the Canaanite language, and as such is cognate with ''gimel'' ג of the Hebrew alphabet. Based on its name, the letter has been interpreted as an abstract representation of a camel ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
