Effects of speaking style on the shape of fundamental frequency distributions

The present study has two main goals. The first is to describe the effects of three speaking styles (spontaneous interview, sentence reading and word list reading) on statistical estimators of fundamental frequency (f0) variability (mean, standard deviation, skewness and kurtosis) in five female and five male speakers of Brazilian Portuguese (BP). Most f0 contours of word reading are bimodal. Analysis of their time-normalized contours suggests this is caused by the time-compressed realization of fast transitions from low to high or high to low tones aligned with stressed syllables. Considering only unimodal distributions, results show that there are no statistically significant effects in the male data for any of the four variability estimators. Effects show up in female data. Spontaneous style has statistically significant higher mean, SD and skewness than read speech. Findings in the previous literature indicate the reverse pattern, though, for languages other than BP. The second goal of the study is to characterize the statistical properties of f0 distributions beyond mean and SD. Results confirm previous observations that most f0 distributions have positive skewness, are left-tailed and have kurtosis values that deviate significantly from the normal because of large deviations from the central or modal value. A distribution fitting procedure tested six distributions. The asymmetric Burr type XII distribution emerges as the one that best fits the data in the corpus. Results show that two of the parameters that determine its shape correlate well with the empirical f0 distribution values of SD and skewness. Important effects of speaking style on f0 seen in female speakers can be reproduced by combinations of the Burr distributions’ parameters.

Generating Distribution Functions Based on Burr Differential Equation

One of the most prominent families of statistical distributions is the Burr’s system. Recent renewed interest in developing more flexible statistical distributions led to the re-examination of Burr’s system. Solutions of Burr differential equation are expressed in terms of distribution functions. Burr [1] considered only 12 distribution functions known in literature as the Burr system of distributions, yet there are more than that in number. Studying the Burr system, it was realized that 9 of the Burr distributions are powers of cdf ′s, popularly now known as exponentiated distributions. The remaining 3 are direct solutions in terms of cdf′s. Detailed studies using generator approach techniques to generate Burr distributions has not been undertaken in literature. This motivated us to generalize solutions of Burr differential equation by generator approach. With this aim in mind, beta generator method, exponentiated generator method and beta-exponentiated generator method (a combination of beta and exponentiated generator methods) was proposed. However in this paper, we will focus on exponentiated generator technique as it generates cdf ′s. The other two generator approach techniques generate pdf′s and distributions of order statistics.

A Mixture of Inverse Weibull and Inverse Burr Distributions: Properties, Estimation, and Fitting

The new mixture model of the two components of the inverse Weibull and inverse Burr distributions (MIWIBD) is proposed. First, the properties of the investigated mixture model are introduced and the behaviors of the probability density functions and hazard rate functions are displayed. Then, the estimates of the five-dimensional vector of parameters by using the classical method such as the maximum likelihood estimation (MLEs) and the approximation method by using Lindley’s approximation are obtained. Finally, a real data set for the proposed mixture model is applied to illustrate the proposed mixture model.

METHODOLOGICAL PROBLEMS IN SIMULATION OF THE AGRO-ECOSYSTEMS

Simulation models describe the functioning of agro-ecosystems and the flow of processes in them using computer programs. With their help can be made computer experiments and to predict the behavior of agro-ecosystems. One of the main problems in the creation of simulation models is imitation of uncontrollable soil and weather factors. A number of studies of soil properties and meteorological characteristics indicate that these stochastic variables do not follow the normal (Gaussian) distribution. In the selection of statistical models that approximate the distribution of such stochastic variables, the most appropriate is a family of Johnson distributions. The article examines ways to generate pseudorandom numbers from Johnson and Burr distributions families for simulating soil and weather factors determining agro-ecosystems.

Truncated Life Test Plans for Economic Reliability Based on Four-Parametric Burr Distribution

Burr distribution is considered as a probability model for the lifetime of products. Reliability test plans are those sampling plans in which items from a lot are put to test to make conclusions on the estimate of life, and hence acceptance or rejection of the submitted lot is done. A test plan designs the termination time of the experiment and the termination number for a given sample size and producer’s risk. Tables and graphs were provided for certain specific values of designs, and it is useful to verify the optimum reliability test plan realized by Burr distributions.

A Method for Simulating Burr Type III and Type XII Distributions through -Moments and -Correlations

This paper derives the Burr Type III and Type XII family of distributions in the contexts of univariate -moments and the -correlations. Included is the development of a procedure for specifying nonnormal distributions with controlled degrees of -skew, -kurtosis, and -correlations. The procedure can be applied in a variety of settings such as statistical modeling (e.g., forestry, fracture roughness, life testing, operational risk, etc.) and Monte Carlo or simulation studies. Numerical examples are provided to demonstrate that -moment-based Burr distributions are superior to their conventional moment-based analogs in terms of estimation and distribution fitting. Evaluation of the proposed procedure also demonstrates that the estimates of -skew, -kurtosis, and -correlation are substantially superior to their conventional product moment-based counterparts of skew, kurtosis, and Pearson correlations in terms of relative bias and relative efficiency—most notably when heavy-tailed distributions are of concern.