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.

The effects of cadence and power output upon physiological and biomechanical responses to incremental arm-crank ergometry

The aim of this study was to examine the effects of cadence and power output on physiological and biomechanical responses to incremental arm-crank ergometry (ACE). Ten male subjects (mean +/- SD age, 30.4 +/-5.4 y; height, 1.78 +/-0.07 m; mass, 86.1 +/-14.2 kg) undertook 3 incremental ACE protocols to determine peak oxygen uptake (VO2 peak; mean of 3 tests: 3.07 +/- 0.17 L.min-1) at randomly assigned cadences of 50, 70, or 90 r.min-1. Heart rate and expired air were continually monitored. Central (RPE-C) and local (RPE-L) ratings of perceived exertion were recorded at volitional exhaustion. Joint angles and trunk rotation were analysed during each exercise stage. During submaximal power outputs of 50, 70, and 90 W, oxygen consumption (VO2) was lowest for 50 r.min-1 and highest for 90 r.min-1 (p < 0.01). VO2 peak was lowest during 50 r.min-1 (2.79 +/-0.45 L.min-1; p < 0.05) when compared with both 70 r.min-1 and 90 r.min-1 (3.16 +/-0.58, 3.24 +/-0.49 L.min-1, respectively; p > 0.05). The difference between RPE-L and RPE-C at volitional exhaustion was greatest during 50 r.min-1 (2.9 +/- 1.6) when compared with 90 r.min-1 (0.9 +/- 1.9, p < 0.05). At VO2 peak, shoulder range of motion (ROM) and trunk rotation were greater for 50 and 70 r.min-1 when compared with 90 r.min-1 (p < 0.05). During submaximal power outputs, shoulder angle and trunk rotation were greatest at 50 r.min-1 when compared with 90 r.min-1 (p < 0.05). VO2 was inversely related to both trunk rotation and shoulder ROM during submaximal power outputs. The results of this study suggest that the greater forces required at lower cadences to produce a given power output resulted in greater joint angles and range of shoulder and trunk movement. Greater isometric contractions for torso stabilization and increased cost of breathing possibly from respiratory-locomotor coupling may have contributed increased oxygen consumption at higher cadences.