**Bulletin of Taras Shevchenko National University of Kyiv. Astronomy, no. 61, p. 25-27 (2020)**

**Mathematical problems associated with errors in estimating distances to galaxies**

**S. Parnovsky, Dr Hab.**

**Taras Shevchenko National University of Kyiv **

**Abstract**

I generate many mock samples for applying the Monte Carlo method in order to estimate the bias of the Hubble constant because of the use of estimates of distances to galaxies determined from statistical dependences. I add errors to the original sample generated according to the Hubble law. In doing so, I use two possible options for generating errors in distance, having a constant relative error. Both are practical, but there are some math problems with them. I discuss their effect on the properties of the mock sample. The application of the standard least squares method is discussed and shown that it leads to an underestimation of the slope in the Hubble law. A formula is derived for calculating this slope using the maximum likelihood method and it is shown that it is applicable only for one of the variants of the sample noising. All estimates were obtained theoretically, without using the results of mock samples processing, which are described in a separate paper.

**Key words
**Statistical methods of data processing, least squares method, maximum likelihood method.

**References
**Parnovsky, S. L. 2020, Visnyk Kyiv. nats. un-tu im. Tarasa Shevchenka. Astronomiia, 61, 20