this case the distribution of the sample takes the form 0)=If(x;.)=(f(x;0) i=1 the first equality due to independence and the second due to the fact that the r.v. are identically distributed A less restrictive form of a sample model in which we call an independent sample, where the identically distributed condition in the random sample is re Definition 4 A set of random variables(X1, X2,..., Xn)is said to be an independent sample Grom f(ri; 01), i= 1, 2, .., respectively, if the r v's X1, X2, .. Xn are indepen- dent. In this case the distribution of the sample takes the form f(r 0)=Tf(x;0) Usually the density function f(:: 81), i= 1, 2,..., n belong to the same family but their numerical characteristics(moments, etc )may differs If we relax the independence assumption as well we have what we can call a non-random sample Definition 5 A set of random variables(X1, X2,.,Xn)I is said to be a non-random sample from f(1, 2,., n; 0) if the r v 's X1, X2, .Xn are non-i.id. In this case the only decomposition of the distribution of the sample possible is f( f(cil ) given To, where f(eiII,,Ti-1; 01), i= 1, 2,.n represent the conditional distri- bution of Xi given X1, X2, ., Xi-1 IHere, we must regard this set of random variables as a sample of size ' one'from a multi- variate point of view.this case the distribution of the sample takes the form f(x1, ..., xn; θ) = Yn i=1 f(xi ; θ) = (f(x; θ))n the first equality due to independence and the second due to the fact that the r.v. are identically distributed. A less restrictive form of a sample model in which we call an independent sample, where the identically distributed condition in the random sample is re￾laxed. Definition 4: A set of random variables (X1, X2, ..., Xn) is said to be an independent sample from f(xi ; θi), i = 1, 2, ...n, respectively, if the r.v.’s X1, X2, ..., Xn are indepen￾dent. In this case the distribution of the sample takes the form f(x1, ..., xn; θ) = Yn i=1 f(xi ; θi). Usually the density function f(xi ; θi), i = 1, 2, ..., n belong to the same family but their numerical characteristics (moments, etc.) may differs. If we relax the independence assumption as well we have what we can call a non-random sample. Definition 5: A set of random variables (X1, X2, ..., Xn) 1 is said to be a non-random sample from f(x1, x2, ..., xn; θ) if the r.v.’s X1, X2, ...Xn are non-i.i.d.. In this case the only decomposition of the distribution of the sample possible is f(x1, ..., xn; θ) = Yn i=1 f(xi |x1, ..., xi−1; θi) given x0, where f(xi |x1, ..., xi−1; θi), i = 1, 2, ...n represent the conditional distri￾bution of Xi given X1, X2, ..., Xi−1. 1Here, we must regard this set of random variables as a sample of size ’one’ from a multi￾variate point of view. 3