Spectral index determination between 408 MHz and 5 GHz in the northern sky

We present the joint analysis of two 5-GHz interferometric surveys of the northern sky, taken with different baselines. The two surveys were carried out on the Jodrell Bank 5-GHz interferometer based at Manchester. The Maximum Entropy Method is used to check the consistency of the two surveys and the final two-dimensional maps are used, together with low-frequency full sky surveys, to put constraints on the Galactic spectral index. It is found that synchrotron emission is the dominant process at high Galactic latitudes below 5 GHz.     

A computer method to calculate the convolution of statistical distributions

It is becoming increasingly important to determine probability distributions of combinations of random variables. Convolution is a technique by which the distribution of a sum of random variables can be determined. This paper presents some simplifications in order to reduce the numerical integrations and computer time. In addition, the method may be used with empirical nonanalytic distributions. While Monte Carlo methods are also appropriate for calculating the distribution, convolution can give at least as much accuracy as Monte Carlo methods with a reduction in computation. Two applications are presented: one approximates the distribution of percent sand in an area, and the other indicates a method of determining sample size when using the distribution of means to approximate normality.