Sunspots are dark regions, it is appearing in the deepest layer of solar atmosphere "photosphere", and the average number of sunspots has cycle every 11 year approximately. Sunspots cycles were numbered with solar cycle 1 beginning in 1755 and the most recent solar cycle, is cycle 24, began in December, 2008. Many authors used different techniques and precursor methods to forecast solar sunspots cycles. In this work we applied a new statistical method "autoregressive integrated moving average Models (ARIMA)" on sunspots number data observed by National Oceanic and Atmospheric Administration (NOAA) during the period 1991-2017 (27 years), we predict the sunspot number for the ending of second brunch of current solar sunspots cycle 24. Our prediction of sunspot numbers was compared with the international sunspot number predicted by National Oceanic and Atmospheric Administration (NOAA). Our predictions of monthly mean sunspot numbers along ending years of present solar cycle 24 are in a good agreement with international sunspots number predictions published by NOAA.
In this paper, statistical distribution functions are developed for distance determination of stellar groups. This method depends on the assumption that absolute magnitudes and apparent magnitudes follow a Gaussian distribution function. Due to the limits of the integrands of the frequency function of apparent and absolute magnitudes, we introduce Case A, B, and C Gaussian distributions. The developed approaches have been implemented to determine distances to some clusters and stellar associations. The comparison with the distances derived by different authors reveals good agreement.
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