Hi Subrata. I am not sure of understanding your question. Are you searching for a theoretical model that permits you to simulate distributions in a broad range and generate artificial data from aleatory generated X values? ... If that is the question I suggest to design Lorenz curves -ordered in descense- with the exponential shape L(X) = X^F(x) ... -in excel notation- (F is a function of X=cummulated fraction of population). Its derivate with respect to Xac produces the variable CDF measured in mediae of the distribution. For example, if F(x)=0.5 constant then you have a Pareto distribution. If F(X) = 0.5-0.2X you get a different distribution. I have studied it starting from theoretical functions F(x) to generate the rest, or counterwise, starting from particular samples and arriving to a proxy particular F function that permits to graph the distribution, fits data and has close isomorphism with data sample. That is the essence of my two decades research but may not answer your question.

In a statistical model for data X with probability distribution depending on a parameter theta, a statistic T=T(X) is sufficient for a parameter theta if the conditional probability distribution of the data X given the value of the statistic T no longer depends on theta. A statistic T is completefor the parameter theta if, for any two functions f and g of the statistic, E(f(T))=E(g(T)) for all theta implies f = g. It follows from this that if some function of T is an unbiased estimator of theta, there are no other functions of T which are also unbiased.

So the definitions can both be given without reference to measure theory at all, and they both have clear probabilistic or statistical meanings. If that is what you mean by "physical" meaning, this should answer your question.

However in order to make these verbal definitions mathematically absolutely precise it is necessary (in general) to add some technical refinements and this is usually done using the language of measure theory. But if you don't want to learn that language, you can get by without it.

If T is sufficient and complete, and kappa is some function of the parameter theta, and g is some function of T such that E(g(T)) = kappa(theta) for all theta, then g(T) is the unique minumum variance unbiased estimator of kappa(theta). The canonical sufficient statistic in a full exponential family is sufficient and complete.