Numerous papers have investigated the distribution of birth weight. This interest arises from the association between birth weight and the future health condition of the child. Birth weight distribution commonly differs slightly from the Gaussian distribution. The distribution is typically split into two components: a predominant Gaussian distribution and an unspecified ‘residual’ distribution. In this study, we consider birth weight data from the Åland Islands (Finland) for the period 1885–1998. We compare birth weight between males and females and among singletons and twins. Our study confirms that, on average, birth weight was highest among singletons, medium among twins, and lowest among triplets. A marked difference in the mean birth weight between singleton males and females was found. For singletons, the distribution of birth weight differed significantly from the normal distribution, but for twins the normal distribution held.

Let Qn denote the number of times where a simple random walk reaches its maximum, where the random walk starts at the origin and returns to the origin after 2n steps. Such random walks play an important role in probability and statistics. In this paper the distribution and the moments of Qn, are considered and their asymptotic behavior is studied.