Re: Gaussian

Kaushik wrote:

if X,Y are iid normals ~N(0,sigma^2) does X^2+Y^2 follow and known
distribution. if sigma=1 this is chi-square distribution but for sigma
other than 1 does it follow an known distribution whose pdf is known?


X^2 + Y^2 has exponential distribution with parameter 1 / (2 sigma^2). Note that the chi-sqaured distribuition with n degrees of freedom is the same as the gamma distribution with shape parameter n/2 and scale parameter 1/2.

--
Stephen J. Herschkorn sjherschko@xxxxxxxxxxxx
Math Tutor on the Internet and in Central New Jersey and Manhattan

.

Relevant Pages

  • Re: Multinomial approximation to Poisson ??
    ... how does one determine the probabilities of the ... Any references, suggestions? ... of the Poisson to the Chi-Square distribution. ...
    (sci.stat.math)
  • Re: Chi-square statistic
    ... to have the chi-square distribution. ... The rate of approximation ... Herman Rubin, Department of Statistics, Purdue University ...
    (sci.stat.consult)
  • Re: Question relating to order statistics of normal random variables
    ... (similar to order statistics, except that we are using the absolute ... Because of the symmetry of Naround 0, you distribution of!X! ... An exponential is a Chi-square distribution with 2 d.f.. ... use the quantile function to give values in terms ...
    (sci.stat.math)
  • Complaint About Statistics Toolbox Documentation
    ... is the probability that a single observation from a chi^2 distribution ...
    (comp.soft-sys.matlab)
  • Re: distance between points from 2d normal distribution
    ... used the formula for chi-square distribution of order 2 to get ... But this is the distribution for D^2 isn't it? ... negative exponential curve but a simulation for distances ... My desire is to analytically get the distribution for the latter, ...
    (comp.soft-sys.matlab)