Chi-squared Distribution - Definition

Definition

If Z1, ..., Zk are independent, standard normal random variables, then the sum of their squares,

Q\ = \sum_{i=1}^k Z_i^2,

is distributed according to the chi-squared distribution with k degrees of freedom. This is usually denoted as

Q\ \sim\ \chi^2(k)\ \ \text{or}\ \ Q\ \sim\ \chi^2_k .

The chi-squared distribution has one parameter: k — a positive integer that specifies the number of degrees of freedom (i.e. the number of Zi’s)

Read more about this topic:  Chi-squared Distribution

Famous quotes containing the word definition:

    “According to our social pyramid, all men who feel displaced racially, culturally, and/or because of economic hardships will turn on those whom they feel they can order and humiliate, usually women, children, and animals—just as they have been ordered and humiliated by those privileged few who are in power. However, this definition does not explain why there are privileged men who behave this way toward women.”
    —Ana Castillo (b. 1953)

    “... we all know the wag’s definition of a philanthropist: a man whose charity increases directly as the square of the distance.”
    —George Eliot [Mary Ann (or Marian)

    “Was man made stupid to see his own stupidity?
    Is God by definition indifferent, beyond us all?
    Is the eternal truth man’s fighting soul
    Wherein the Beast ravens in its own avidity?”
    —Richard Eberhart (b. 1904)