Consider an exponential family such that the variance function is given by the power of the mean function. This family is denoted by EDα if the variance function is given by μ(2-α)/(1-α), where μ is the mean function. When 0≤α<1, it is known that the transformation of ED(α) to normality is given by the power transformation X(1-2α)/(3-3α), and conversely, the power transformation characterizes ED(α). Our principal concern will be to show that this power transformation has an another merit, i.e., the density of the transformed variate has an absolutely convergent Gram-Charier expansion.
|Number of pages||14|
|Journal||Annals of the Institute of Statistical Mathematics|
|Publication status||Published - Mar 1 1993|
All Science Journal Classification (ASJC) codes
- Statistics and Probability