The art of parameter(s) induction to the baseline distribution has received a great deal of attention in recent years. The induction of one or more additional shape parameter(s) to the baseline distribution makes the distribution more flexible especially for studying the tail properties. This parameter(s) induction also proved helpful in improving the goodness-of-fit of the proposed generalized family of distributions. There exist many generalized (or generated) G families of continuous univariate distributions since 1985. In this paper, the well-established and widely-accepted G families of distributions like the exponentiated family, Marshall-Olkin extended family, beta-generated family, McDonald-generalized family, Kumaraswamy-generalized family and exponentiated generalized family are discussed. We provide lists of contributed literature on these well-established G families of distributions. Some extended forms of the Marshall-Olkin extended family and Kumaraswamy-generalized family of distributions are proposed.

Motivated by time series analysis, we consider the problem of solving the recurrence relation u n+1 = v n+1 + u n ⊗ v n for n ≠ 0 and u n, given the sequence v n. A solution is given as a Bell polynomial. When v n can be written as a weighted sum of nth powers, then the solution u n also takes this form. Mathematical subject classification: 33E99.

Motivated by time series analysis, we consider the problem of solving the recurrence relation u n+1 = v n+1 +u n⊗v n for n ≠ 0 and u n, given the sequence v n. A solution is given as a Bell polynomial. When v n can be written as a weighted sum of nth powers, then the solution u n also takes this form. Mathematical subject classification: 33E99.

O presente trabalho publicado por Miranda de Sá (2004) derivou pela primeira vez, a distribuição de amostras de coerência estimada entre dois sinais. Este artigo apresenta temas computacionais relacionados a distribuição de amostras, utilizando métodos de aproximação. Nesta nota, apresentamos vários programas "on line" computação exata de medidas de distribuição de amostras. São discutidas as vantagens destes programas.

The recent paper published by Miranda de Sa (2004) derived, for the first time, the sampling distribution of coherence estimated between two signals. The paper also considered computational issues of the sampling distribution, using an approximate method. In this short note, we provided several 1-line programs for the exact computation of various measures of the sampling distribution. The advantages of using these programs are discussed.