Statistical distances of the northern sky bright K and M dwarfs with apparent magnitude J < 9

In this paper, we estimate distances and generate the mean absolute magnitudes and dispersions for K and M bright dwarfs using two different approaches. The methods are based on the assumption that the absolute and apparent magnitude follows the exponential and Gaussian distributions functions. The effect of Malmquist bias has been studied to show how effective bias is in comparison. We found that the range between the calculated distances for the spectral subtypes K is small (2.6 pcs), while the range in the distance of the spectral subtypes M is a little big (21.6 pcs), and this may be due to the different chemical compositions and evolution scenarios for each spectral subtype. This means that these dwarfs are situated in the same cloud as near and far sides. We spread the dwarfs above and below the galactic plane to gain certain physical properties based on the statistical study and also on the spectral subtypes. The estimated distances from the two approaches are approximately the same but there are noticeable differences between the generated mean absolute magnitudes and dispersions.