This paper presents an LDA-style topic model that captures not only the low-dimensional structure of data, but also how the structure changes over time. Unlike other recent work that relies on Markov assumptions or discretization of time, here each topic is associated with a continuous distribution over timestamps, and for each generated document, the mixture distribution over topics is influenced by both word co-occurrences and the document's timestamp. Thus, the meaning of a particular topic can be relied upon as constant, but the topics' occurrence and correlations change significantly over time. We present results on nine months of personal email, 17 years of NIPS research papers and over 200 years of presidential state-of-the-union addresses, showing improved topics, better timestamp prediction, and interpretable trends.

/pdf/topics-over-time-a-non-markov-continuous-time-model-of-3lvv7erdi9.pdf

Topics over time: a non-Markov continuous-time model of topical trends

Kumaraswamy [Generalized probability density-function for double-bounded random-processes, J. Hydrol. 462 (1980), pp. 79–88] introduced a distribution for double-bounded random processes with hydrological applications. For the first time, based on this distribution, we describe a new family of generalized distributions (denoted with the prefix ‘Kw’) to extend the normal, Weibull, gamma, Gumbel, inverse Gaussian distributions, among several well-known distributions. Some special distributions in the new family such as the Kw-normal, Kw-Weibull, Kw-gamma, Kw-Gumbel and Kw-inverse Gaussian distribution are discussed. We express the ordinary moments of any Kw generalized distribution as linear functions of probability weighted moments (PWMs) of the parent distribution. We also obtain the ordinary moments of order statistics as functions of PWMs of the baseline distribution. We use the method of maximum likelihood to fit the distributions in the new class and illustrate the potentiality of the new model with a...

/pdf/a-new-family-of-generalized-distributions-1jh9brns7x.pdf

A new family of generalized distributions

In this paper, a new method is proposed for generating families of continuous distributions. A random variable $$X$$
 , “the transformer”, is used to transform another random variable $$T$$
 , “the transformed”. The resulting family, the $$T$$
 -
 $$X$$
 family of distributions, has a connection with the hazard functions and each generated distribution is considered as a weighted hazard function of the random variable $$X$$
 . Many new distributions, which are members of the family, are presented. Several known continuous distributions are found to be special cases of the new distributions.

/pdf/a-new-method-for-generating-families-of-continuous-2e75jsuwp2.pdf

A new method for generating families of continuous distributions

Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages

For the first time, we introduce and study some mathematical properties of the Kumaraswamy Weibull distribution that is a quite flexible model in analyzing positive data. It contains as special sub-models the exponentiated Weibull, exponentiated Rayleigh, exponentiated exponential, Weibull and also the new Kumaraswamy exponential distribution. We provide explicit expressions for the moments and moment generating function. We examine the asymptotic distributions of the extreme values. Explicit expressions are derived for the mean deviations, Bonferroni and Lorenz curves, reliability and Renyi entropy. The moments of the order statistics are calculated. We also discuss the estimation of the parameters by maximum likelihood. We obtain the expected information matrix. We provide applications involving two real data sets on failure times. Finally, some multivariate generalizations of the Kumaraswamy Weibull distribution are discussed.

P. Kumaraswamy

Papers

A generalized probability density function for double-bounded random processes