Abstract
This paper discusses the fundamental contribution of the quantum theory to theoretical statistics. The paper presents and discusses the key moment of the first quantization. It looks at the relationship of the mean and the variance to energy. It then describes and analyzes Planck's procedure. Finally, the paper discusses the statistical meaning of the procedure to quantum physics.

Table of Contents:
Abstract
Introduction
First Example of Quadratic Variance Distributions
Introducing Correlations: an Interpretation of Quantum
Formal Description of the Quadratic Variance Ensembles
Conclusions

From the Paper
"The fact that statistical physics can be taken as a particular type of statistical inference does not seem to play too much of a theoretical role in physics today. It is perhaps the strong suggestion of subjectivity associated with the concept of inference that determines physicists to rely mostly upon kinetic basis of statistical laws. However, recognized or not, the statistical inference has played a very important part in such fundamental problems like building physical concepts. One illustrative example is the concept of quantum. Originally related to the frequency property of light, it was in time explained as associated with its particle properties, then with the temperature of light. All these properties can be traced logically back to the particular type of statistics which is fundamental for the ensembles characterizing the black body radiation. More than this, that very type of statistics is essential in the contemporary sophisticated descriptions of the squeezed states and their related concepts. This essay presents details of the statistics involved in the history of quantum, and the essential points of this history."

Tags:distributions, exponential, Gaussian, Blacbody, Radiation, Poincare, Thermal