On the Characteristic Functions of the Distributions of Estimates of Various Deviations in Samples from a Normal Population
Kac, M.
Ann. Math. Statist., Tome 19 (1948) no. 4, p. 257-261 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
An explicit formula for the characteristic function of the deviation $\frac{1}{n} \sum_n {k=1}\|X_k - \bar X\|^\alpha,\quad\alpha > 0,$ is derived for samples from a normal population. For $\alpha = 1$ one can calculate the probability density function but the result does not seem to be in complete agreement with a recent formula of Goodwin [1].
Publié le : 1948-06-14
Classification:  
@article{1177730250,
     author = {Kac, M.},
     title = {On the Characteristic Functions of the Distributions of Estimates of Various Deviations in Samples from a Normal Population},
     journal = {Ann. Math. Statist.},
     volume = {19},
     number = {4},
     year = {1948},
     pages = { 257-261},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177730250}
}

Kac, M. On the Characteristic Functions of the Distributions of Estimates of Various Deviations in Samples from a Normal Population. Ann. Math. Statist., Tome 19 (1948) no. 4, pp.  257-261. http://gdmltest.u-ga.fr/item/1177730250/