A Double Truncated Binomial Model to Assess Psychiatric Health through Brief Psychiatric Rating Scale: When is Intervention Useful?

A double truncated binomial distribution model with ‘u’ classes truncated on left and ‘v’ classes truncated on right is introduced. Its characteristics, namely, generating functions; and the measures of skewness and kurtosis have been obtained. The unknown parameter has been estimated using the method of maximum likelihood and the method of moments. The confidence interval of the estimate has been obtained through Fisher’s information matrix. The model is applied on cross sectional data obtained through Brief Psychiatric Rating Scale (BPRS) administered on a group of school going adolescent students; and the above-mentioned characteristics have been evaluated. An expert, on the basis of the BPRS score values, suggested an intervention program. The BPRS scores of the students who could be administered the intervention program lied in a range (which was above the lowest and below the highest possible values) suggested by the expert. Whereas the complete data suggested the average number of problem areas is four (which was not in consonance with the observations given by the expert), the double truncated model suggested the number of such areas as five which was consistent with the observations made by the expert. This establishes the usefulness of double truncated models in such scenarios.