Bøger af Soubhik Chakraborty

Outliers have been regarded as the noisy data in statistics which have now turned out to be an important problem and are now been researched in diverse fields and application domains. Outlier detection has been in core interest of not only the statisticians but all the professionals who are working on a particular data set. Many outlier detection techniques have been developed specific to certain application domains, while some techniques are more generic. This work has added one more technique to the bucket list of all those professionals. Power mean which has been used as a general method to calculate various means like arithmetic mean (power mean with power 1), geometric mean (power mean with power 0), Lorentz mean (power mean with power 1/3) etc. can also be used to detect the sensitivity of the data towards being the outlier. This work studies various powers of power mean for outlier detection. It contains two different data sets, one containing fractions and the other integers. The results have been verified by the existing standard techniques of outlier detection. Thus this book contains description of detecting outliers using power mean with different types of data sets, graphs and figures for better understanding. The idea is to check the efficacy of the method using a data set in which the outlier or the anomaly is already known and then testing the same method for a data set in which the outliers are not known to us. The open research issues and challenges at the end will provide researchers a clear path for the future of outlier detection methods. The book would be useful for practitioners of applied statistics and data analysts.

Master's Thesis from the year 2019 in the subject Musicology - Miscellaneous, grade: 8.5, , language: English, abstract: The present work attempts to study the impact of Hindustani Classical Music on Bollywood in a legitimate manner using a statistical approach emphasizing on statistical modeling of musical structure and performance and other statistical features such as note duration and inter onset interval with a case study in raga Yaman.Any music originates in the society and develops with the changing realities of it. It accepts new and modifies the existing cultural norms in different periods of time. This process of acceptance and rejection makes any form of art exist for long. Inspite of all this, in various phases, Hindustani classical music, being the base of many popular Bollywood songs has helped in their popularity and lifelong existence because of the strong focus on melody. A raga, which is the nucleus of Indian classical music, be it Hindustani or Carnatic, is a melodic structure with fixed notes and a set of rules which characterize a certain mood conveyed by erformance. Hindustani ragas have embraced the elements of several Bollywood songs, which has given these songs a strong impact despite the strong influence of western art music in Bollywood music industry. The present work attempts to study this impact in a legitimate manner using a statistical approach emphasizing on statistical modeling of musical structure and performance and other statistical features such as note duration and inter onset interval with a case study in raga Yaman. It turns out that the same statistical model for both the raga bandishand a song based on the same raga, i.e., Yaman, an evening raga of the Kalyan thaat.

Master's Thesis from the year 2019 in the subject Mathematics - Stochastics, grade: 8.5, , course: Integrated MSc in Mathematics and Computing, language: English, abstract: We are interested in the behaviour of a determinant with i.i.d. random variates as its elements. A probabilistic analysis has been done for such determinants of orders 2 and 3. We have considered some of the well known distributions, namely, discrete uniform, Binomial Poisson, continuous uniform, standard normal, standard Cauchy and exponential. We are able to give fiducial limits for the determinant using Chebyshev¿s inequality for all the distributions discussed in the text (except standard Cauchy distribution for which expectation does not exist). The main objective is to find the probability distribution of the determinant when its elements are from any of the distributions stated above. The desired distribution has been approximated using the method of transformation in general but when this method could not produce desired results we relied on empirical results based on simulation.

Doctoral Thesis / Dissertation from the year 2019 in the subject Musicology - Miscellaneous, grade: NA, , language: English, abstract: The aim of the research work presented in this book, is to find important features of the music signal so that we can classify the raga into different category. It will encourage the scientific research in Indian Classical music, specifically Hindustani music.The main objectives of the study include:¿ Extraction of features of a music signal which are relevant for classification of the music signal using different techniques.¿ To determine whether the artists singing the raga during a concert belongs to same gharana or different gharanas by finding the MFCC (Mel frequency cepstral co-efficients ) features of a music signal. Andrew plot is used to study the results.¿ Comparison between two types of ragas, one being aesthetically known to be restful raga and the other restless in nature is done by finding statistical features. Distinction between the two types of raga is done by finding the mean, standard deviation and Inter onset interval. The Transitory and non-transitory frequency movements between the notes of both ragas is determined.¿ Statistical Modeling of ragas is done to distinguish between Restful ragas and Restless Ragas. Simple Exponential smoothing techniques is used for Modeling the Restless Ragas Pilu and Bhairavi and Double exponential Smoothing techniques is used for Modeling the Restful Raga Todi .¿ The work is focused on music emotion representation. The characteristics features of music signal such as rhythm, melody, pitch and timbre are studied. Among these which parameter(s) play a major role in creating happy or sad emotion in the song or music samples are studied.

The book opens with a short introduction to Indian music, in particular classical Hindustani music, followed by a chapter on the role of statistics in computational musicology.

It begins with an in-depth introduction to musical signal analysis and its current applications, and then moves on to a detailed discussion of the features involved in understanding the musical meaning of the signal in the context of Hindustani music.