Probabilities of Misclassification Linked with Inverse Hyperbolic Sine Normal (IHSN) Distribution

Probability of misclassification occurs when there is a choice of criteria that is not favourable for classification. The probabilities of misclassification associated with a family of Johnson’s system, the Inverse Hyperbolic Sine Normal distribution, was developed in this study. The distribution theory and rules, along with the formulation of the system, were generated. It was asserted that the estimation of the parameters of the system could be demystified if one or more variables under consideration are distributed normally.

A Note on Different Types of Probabilities of Misclassification

Whenever a discriminant function is constructed, the attention of a researcher is often focused on classification. The underlined interest is how well does a discriminant function perform in classifying future observations correctly. In order to assess the performance of any classification rule, probabilities of misclassification of a discriminant function serves as a basis for the procedure. Different forms of probabilities of misclassification and their associated properties were considered in this study. The misclassification probabilities were defined in terms of probability density functions (pdf) and classification regions. Apparent probability of misclassification is expressed as the proportion of observations in the initial sample which are misclassified by the sample discriminant function. Different methods of estimating probabilities of misclassification were related to each other using their individual shortcomings. The status of degrees of uncertainties associated with probabilities of misclassification and their implications were also specified.

Scoring rules, and the role of chance: Analysis of the 2008 World Fly Fishing Championships

We analyze the 2008 World Fly Fishing Championships data to examine two issues: (I) changes to scoring rules are proposed so that catching bigger fish is no longer a disadvantage; and (II) the relative role of chance versus competitor skill in determining the competition outcomes is investigated. For (I), a new quadratic polynomial formula for the number of points awarded for a fish of a certain length meant that the competitor who caught the biggest fish in one of the rivers was no longer disadvantaged, during the 20-min period it took to land the fish, compared to those anglers who caught many small fish. For (II), it was found that an angler A, who is actually better than angler B, has an approximate probability of 8.5% of having, overall, a worse score than angler B. By increasing the number of fishing sessions from five to seven, the probability of misclassification drops to about 7%. Other topics, such as the advantages of the proposed formula and the various fishing strategies, are also discussed.