By N. Balakrishnan

ISBN-10: 0471427985

ISBN-13: 9780471427988

Designed as an creation to statistical distribution theory.* contains a first bankruptcy on simple notations and definitions which are necessary to operating with distributions.* ultimate chapters are divided into 3 components: Discrete Distributions, non-stop Distributions, and Multivariate Distributions.* routines are included during the textual content that allows you to improve realizing of fabrics simply taught.

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Extra resources for A primer on statistical distributions

Sample text

X , 2 ) = P { X n 5 x}, respectively. Moreover, ariy set of n random variables X I , . . , X,, forms a random vector X = ( X I , .. , X,). Hence, F ( x ) = F ( z 1 , .. , 2 , ) = P{X1 5 51,. ;x,5 2 , } . is often called t,he joint distribution, function of the variables X I ,. . X,. sily. rnple, we have , x, 5 z:7n}= F ( s 1 , . . as the joirit distribution function of (XI,. X,,,,w . . ; m ) . ,X T n ) . ndom variables X I . . re said to be independ e n t random! variables if P(X1 5 2 1 , .

K-1, where a is any real value and h > 0 is the step of the distribution. Sometimes, such a distribution is called a discrete rectangular distribution. The linear transformations of random variables enable us to consider, without loss of generality, just the standard discrete uniform distribution taking on values 0 , 1 , . . , k - 1, which correspond to a = 0 and h = 1. Note that the case when a = 0 and h = l / k is also important, but it can be obtained from the standard discrete uniform distribution by means of a simple scale change.

Te case (71 = 2 ) . 90) (y) d y , respectively. Then, the following properties of easily: (13 8 ) f ~ , (s. riable X + (d) f x , Y ( s , t ) = f x ( . 24 Let P ( s , t ) be the gerieratirig function of the random vector ( X . Y ) . t , 7 ~ ) of the rantlorn vector ( 2 X 1. r;, 2Y). 15 Transformations of Variables a:r, ax1 ~ ~ 3Yl aY2 d:Yl dYz ... a22 _ _ _ _8x2 _ J = a& ~ dyl ax 1 __ 8YTl 852 __ dYrl ... 11, ~ dY2 ... t,ion. 92) by integrating out the other variables. y B1,. . , Be, then we can construct l sets of one-to-one transformations (one for each Bi)and their respect,ive Jxobians, and then finally express the tleiisity function of the vector Y = (Yl...