Statistical Analysis and Modeling of the High-Energy Proton Data from the Telstar I Satellite

TECHNICAL VOLUME X L v r Copyright © 1967, SEPTEMBER 1967 .American Telephone JOURNAL NUMBER and Telegraph Company 7 Statistical Analysis and Modeling of the High-Energy Proton Data From the Telstar® 1 Satellite By J. D. GABBE, M. B. WILK and W. L. BROWN (Manuscript received October 4, 1966) This paper deals with the analysis of data jrom the omnidirectional high-energy proton detector on the Telstar® 1 satellite. The main accomplishment is the development of relatively simple (empirical) mathematical models which give a statistically accurate representation of the measured spatial distribution of intensity of protons with energies between 50 and 130 MeV. These models depend upon the fitting of 8 (or 9 or 10) coefficients based on samples containing approximately 1000 of the nearly 80,000 experimental observations. The nature of the model for the average omnidirectional counting rate permits its closed form transformation to the equivalent equatorial pitch angle distribution. Sufficiently accurate fits were achieved so that the residuals (equal to observed minus fitted) could be productively examined for possible dependence on variables other than the two magnetic coordinates used in the fitting. One consequence of this ivas the detection of instrumental susceptibility to temperature and bias voltage changes, which led to an objective partitioning of the data. The present paper has several evolutionary aspects: In particular, a series of one-dimensional fits was employed as a base for developing a two-dimensional model; a preliminary analysis of all the data ivas used to guide the rejection of outliers; a first two-dimensional fit to all the data 1301 1302 T H E BELL SYSTEM TECHNICAL JOURNAL, SEPTEMBER 1 9 » 7 led to a data-independent basis for -partitioning the data; the mode of selection of a sample of data, to which the two-dimensional model was fitted, changed as deeper insight into the importance of this issue developed; and, after a very satisfactory fit to the data was attained, the model was improved by specialization and reparameterization so as to overcome some statistical defects and to achieve greater physical meaning.