Алгоритм побудови послідовності значень випадкової величини, що має сингулярний розподіл салемівського типу

Abstract

In the paper we describe algorithm to obtain a sequence of values of
random variable $\xi$ with independent identically distributed binary
digits having a singular distribution of Salem type. Some examples of
application of this algorithm are also given. We consider distribution
of $\xi$ as one-parameter distribution that depends on parameter
$\rho= \mathbb{P} \{ \alpha_i =1 \}$, where $\alpha_i$ is a $i$th
binary digit of $\xi$. For samples obtained by simulation modeling, we
demonstrate three methods for estimation of unknown parameter $\rho$:
method of moments, modified minimum distance estimation and
maximum-likelihood estimation methods. We also compare accuracy of
obtained estimators.