Bivariate Transmuted Burr Distribution: Properties and Application

The bivariate distributions are useful in simultaneous modeling of two random variables. These distributions provide a way of modeling complex joint phenomenon. In this article, a new bivariate distribution is proposed which is known as the bivariate transmuted Burr (BTB) distribution. This new bivariate distribution is extension of the univariate transmuted Burr (TB) distribution to two variables. The proposed BTB distribution is explored in detail and the marginal and conditional distributions for the distribution are obtained. Joint and conditional moments alongside hazard rate functions are obtained. The maximum likelihood estimation (MLE) for the parameters of the BTB distribution is also done. Finally, real data application of the BTB distribution is given. It is observed that the proposed BTB distribution is a suitable fit for the data used.

Statistical modelling of bus travel time with Burr distribution

A better understanding of the travel time distribution shape or pattern could improve the decision made by the transport operator to estimate the travel time required for the vehicle to travel from one place to another. Finding the most appropriate distribution to represent the day-to-day travel time variation of an individual link of a bus route is the main purpose of this study. Klang Valley, Malaysia is the study area for the research. A consecutive of 7 months ten bus routes automatic vehicle location (AVL) data are used to examine the distribution performance. The leading distribution proposed for the research is the Burr distribution. Both symmetrical and asymmetrical distributions that have been proposed in existing studies are also used for comparison purposes. Maximum likelihood estimation is applied for parameter estimation while loglikelihood value, Akaike information criterion (AIC) and Bayesian information criterion (BIC) are applied for performance assessment of the distributions. Promising results are obtained by the leading model in all different kinds of operating environment and could be treated as the preliminary preparation for further reliability analysis.

Longitudinal Acceleration Models for Horizontal Reverse Curves of Two-Lane Rural Roads

The operating speed profile models adopt acceleration and deceleration as constant values obtained from kinematic models, assuming that the operating speeds between two consecutive sections are not spatially correlated. Existent research shows that acceleration and deceleration in horizontal reverse curves (HRC) depend on the tangent length and curve radii. In this paper, accelerations/decelerations-geometry models for light cars are proposed. The models are based on the data obtained in-field with a 10 Hz GPS under favourable traffic, weather, and pavement condition to isolate the effect of road geometry over the speed changes. The models were calibrated using the 95th percentile of acceleration probability density function (pdf) obtained section to section in the HRC. It was found that the acceleration and deceleration pdf follow the Burr distribution. Therefore, a Box–Cox transformation is needed to properly calibrate acceleration-geometry models. The models obtained confirmed that accelerations and decelerations depend on the radius of entrance and departure curves of the HRC. The results contribute to better understanding of the acceleration/deceleration patterns of light cars and to enhancing operating speed models in the HRC.

MATHEMATICAL PROPERTIES AND APPLICATIONS OF MINIMUM GUMBEL BURR DISTRIBUTION

This paper presents the details of a proposed continuous model for the minimum Gumbel Burr distribution which is based on four different parameters. The model is obtained by compounding the Gumbel type-II and Burr-XII distributions. Basic mathematical properties of the new distribution were studied including the quantile function, ordinary and incomplete moments, moment generating function, order statistics, Rényi entropy, stress-strength model and stochastic ordering. The parameters of the proposed distribution are estimated using the maximum likelihood method. A Monte Carlo simulation was presented to examine the behaviour of the parameter estimates. The flexibility of the proposed model was assessed by means of three applications.