  Credit estimation and bankruptcy prediction methods have been utilizing
Altman's $z$ score method for the last several years. It is reported in many
studies that $z$ score is sensitive to changes in accounting figures.
Researches have proposed different variations to conventional $z$ score that
can improve the prediction accuracy. In this paper we develop a new
multivariate non-linear model for computing the $z$ score. In addition we
develop a new credit risk index by fitting a Pearson type-III distribution to
the transformed financial ratios. The results from our study have shown that
the new $z$ score can predict the bankruptcy with an accuracy of $98.6\%$ as
compared to $93.5\%$ by the Altman's $z$ score. Also, the discriminate analysis
revealed that the new transformed financial ratios could predict the bankruptcy
probability with an accuracy of $93.0\%$ as compared to $87.4\%$ using the
weights of Altman's $z$ score.
