Data noising by finite normal and gamma mixtures with application to the problem of rounded observations

In many real problems, statistical analysis of data containing additional measurement errors, including rounding, is performed, which in some situations can lead to sufficiently significant distortions. In this paper, estimates for an unknown expectation of observations are obtained for one of the possible rounding models under the assumption that the original data are additionally noised with random variables having distributions of the type of finite mixtures of normal and gamma laws. Confidence intervals for an unknown expectation are constructed using the refined estimate for the variance of the integer part of the random variable. An algorithm for determining the value of the parameter of artificial noise, which can be added to the initial data to improve the quality of the method of moving separation of mixtures, is discussed.