Analysis on Difference of Contaminated Normal Distribution PDF

As a very important distribution, contaminated normal distribution play a great role in data processing. The probability density function (PDF) feature of the contaminated normal distribution was investigated. The Kullback-Leibler distance is suggested for measuring PDF difference between mean shift model and variance inflation model. Numerical calculations show that the PDF difference of two kinds of model is related to mean shift parameter λ and the variance inflation factor α closely when the main distribution is the standard normal distribution and the relationship is nonlinear proportional.

Key Characteristics of Hymns

The authors propose a way of patterning the bars of monophonic melodies in hymns and finding keys from such patterns. The authors represent monophonic melody bars on a vector showing the duration of pitch chroma contained in each bar. In experiments, the authors patterned bars of 352 four/four beat hymns, defined the distance between the bar key and melody, and found they key from this, correctly 83.1% of the time. The authors also propose a way to determine the maximum likelihood of a contaminated normal distribution of distance between patterns using an EM algorithm. Key characteristics of hymns were then studied using this method.