Алгоритм побудови послідовності значень випадкової величини, що має сингулярний розподіл салемівського типу
In the paper we describe algorithm to obtain a sequence of values ofrandom variable $\xi$ with independent identically distributed binarydigits having a singular distribution of Salem type. Some examples ofapplication of this algorithm are also given. We consider distributionof $\xi$ as one-paramete...
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| Date: | 2017 |
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| Keywords: | keywords |
| Main Authors: | , |
| Format: | Article |
| Language: | Ukrainian |
| Published: |
Інститут математики НАН України
2017
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| Online Access: | https://trim.imath.kiev.ua/index.php/trim/article/view/401 |
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| Journal Title: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Transactions of Institute of Mathematics of NAS of Ukraine| Summary: | In the paper we describe algorithm to obtain a sequence of values ofrandom variable $\xi$ with independent identically distributed binarydigits having a singular distribution of Salem type. Some examples ofapplication of this algorithm are also given. We consider distributionof $\xi$ as one-parameter distribution that depends on parameter$\rho= \mathbb{P} \{ \alpha_i =1 \}$, where $\alpha_i$ is a $i$thbinary digit of $\xi$. For samples obtained by simulation modeling, wedemonstrate three methods for estimation of unknown parameter $\rho$:method of moments, modified minimum distance estimation andmaximum-likelihood estimation methods. We also compare accuracy ofobtained estimators. |
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