Poisson stochastic process
Several branches of science try to solve the problem of respondents’ behavior rate estimation when only incomplete, uncertain and imprecise data are available.
The paper goal it to describe techniques that can estimate respondents’ behavior rate based on his incomplete and un-certain answers about the participation in it. The secondary goal is to present the model that underlies the estimation procedure. From the mathematical point of view this task renders into the identification of the parameter, which represents the rate of the Poisson stochastic process. This very process is chosen to be the model of the behavior that is considered as a series of its episodes.
The paper also offers formalized representation for all known wordings of respondent’s meaningful answers. Any respondent’s answer should be recognized according the offered representation.
The rate estimate is made based on maximum likelihood principle. It is underlined that answer uncertainty is determined by the means of communication, i.e., by natural language usage. The uncertainty quantified, the rate becomes a random variable that can be studied properly with the tools of the theory of probability. We can numerically calculate mean, standard deviation, range, and interquartile range. An applied problem related to HIV risk measurements is stated; it renders to the studied estimates when we combine the Poisson stochastic process the equation and Bell-Trevino model