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A Lagrangian gamma distribution of the second kind. (English) Zbl 0559.60019

The distribution of the time T for the occurrence of the rth event is derived in a linear function Poisson process, which belongs to a recently introduced family of distributions [cf. the first two authors, SIAM J. Appl. Math. 43, 302-313 (1983; Zbl 0509.60018)], called Lagrangian distributions of the second kind \((LD_ 2)\). In analogy with the ordinary Poisson process, the distribution of the random variable T has been termed the Lagrangian gamma distribution of the second kind \((LG_ 2)\); several of its properties and special cases are studied. The frequency function is graphed for some parameter values.

MSC:

60E05 Probability distributions: general theory

Citations:

Zbl 0509.60018
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References:

[1] and , 1975: A Lagrangian gamma distribution. Statistical Distributions in Scientific Work, Vol. 1, G. P. Patil et al. (eds), pp. 241–246.
[2] Consul, SiamJ. Appl. Math. 23 pp 239– (1972)
[3] Janardan, SIAMJ. Appl. Math. 43 (1983)
[4] Jain, Biom. Z. 17 pp 501– (1975)
[5] Haight, Biometrika 48 pp 167– (1961) · Zbl 0095.12603 · doi:10.1093/biomet/48.1-2.167
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