Incomplete Dirichlet integrals with applications to ordered uniform spacings

Sobel, Uppuluri, and Frankowski, (Selected Tables in Math. Statistics, Vol. IV. Amer. Math. Soc., Providence, R. I., 1977) consider an incomplete Dirichlet integral of type I with several interesting applications connected with the multinomial distribution and provide tables of this integral along with other useful tables. Two incomplete Dirichlet integrals are discussed here along with some useful recurrence relations, providing simple methods of deriving the distribution theory of ordered uniform spacings.