Tree diameter distribution modelling: introducing the logitlogistic distribution

Johnson's SB distribution is a four-parameter distribution that is transformed into a normal distribution by a logit transformation. By replacing the normal distribution of Johnson's SB with the logistic distribution, we obtain a new distributional model that approximates SB. It is analytically tractable, and we name it the "logitlogistic" (LL) distribution. A generalized four-parameter Weibull model and the Burr XII model are also introduced for comparison purposes. Using the distribution "shape plane" (with axes skew and kurtosis) we compare the "coverage" properties of the LL, the generalized Weibull, and the Burr XII with Johnson's SB, the beta, and the three-parameter Weibull, the main distributions used in forest modelling. The LL is found to have the largest range of shapes. An empirical case study of the distributional models is conducted on 107 sample plots of Chinese fir. The LL performs best among the four-parameter models.

Recommendations on the nature of the passenger response time distribution to be used in the MSC 1033 assembly time analysis based on data derived from sea trials

The passenger response time distributions adopted by the International Maritime Organisation (IMO)in their assessment of the assembly time for passanger ships involves two key assumptions. The first is that the response time distribution assumes the form of a uniform random distribution and the second concerns the actual response times. These two assumptions are core to the validity of the IMO analysis but are not based on real data, being the recommendations of an IMO committee. In this paper, response time data collected from assembly trials conducted at sea on a real passanger vessel using actual passangers are presented and discussed. Unlike the IMO specified response time distributions, the data collected from these trials displays a log-normal distribution, similar to that found in land based environments. Based on this data, response time distributions for use in the IMO assesmbly for the day and night scenarios are suggested

Bivariate distribution modeling with tree diameter and height data

The Logit-Logistic (LL), Johnson's SB, and the Beta (GBD) are flexible four-parameter probability distribution models in terms of the (skewness-kurtosis) region covered, and each has been used for modeling tree diameter distributions in forest stands. This article compares bivariate forms of these models in terms of their adequacy in representing empirical diameter-height distributions from 102 sample plots. Four bivariate models are compared: SBB, the natural, well-known, and much-used bivariate generalization of SB; the bivariate distributions with LL, SB, and Beta as marginals, constructed using Plackett's method (LL-2P, etc.). All models are fitted using maximum likelihood, and their goodness-of-fits are compared using minus log-likelihood (equivalent to Akaike's Information Criterion, the AIC). The performance ranking in this case study was SBB, LL-2P, GBD-2P, and SB-2P