Daily rainfall along the United States Pacific Coast appears to conform to a square-root normal probability distribution

EXTRACT (SEE PDF FOR FULL ABSTRACT): As part of a study of climatic influences on landslide initiation, a statistical analysis of long-term (>40 years) records of daily rainfall from 24 Pacific coastal stations, from San Diego to Cape Flattery, disclosed an unexpected result - the square root of the daily rainfall closely approximates a normal distribution function. ... This paper illustrates the use of the square-root-normal distribution to analyze variations in precipitation along the mainland United States Pacific Coast with examples of orographic enhancement, rain shadows, and increase in precipitation frequency with geographic latitude.

On the Skew-Normal-Cauchy Distribution

In this article, we study further properties of a skew normal distribution, called the skew-normal-Cauchy (SNC) distribution by Nadarajah and Kotz (2003). A stochastic representation is obtained which allows alternative derivations for moments, moments generating function, and skewness and kurtosis coefficients. Issues related to singularity of the Fisher information matrix are investigated.

The best are never normal : exploring the distribution of firm performance

Competitive Strategy literature predicts three different mechanisms of performance generation, thus distinguishing between firms that have competitive advantage, firms that have competitive disadvantage or firms that have neither. Nonetheless, previous works in the field have fitted a single normal distribution to model firm performance. Here, we develop a new approach that distinguishes among performance generating mechanisms and allows the identification of firms with competitive advantage or disadvantage. Theorizing on the positive feedback loops by which firms with competitive advantage have facilitated access to acquire new resources, we proposed a distribution we believe data on firm performance should follow. We illustrate our model by assessing its fit to data on firm performance, addressing its theoretical implications and comparing it to previous works.

Gradually truncated log-normal in USA publicly traded firm size distribution

We study the statistical distribution of firm size for USA and Brazilian publicly traded firms through the Zipf plot technique. Sale size is used to measure firm size. The Brazilian firm size distribution is given by a log-normal distribution without any adjustable parameter. However, we also need to consider different parameters of log-normal distribution for the largest firms in the distribution, which are mostly foreign firms. The log-normal distribution has to be gradually truncated after a certain critical value for USA firms. Therefore, the original hypothesis of proportional effect proposed by Gibrat is valid with some modification for very large firms. We also consider the possible mechanisms behind this distribution. (c) 2006 Published by Elsevier B.V.

Quantitative analysis of senile plaques in Alzheimer disease: observation of log-normal size distribution and molecular epidemiology of differences associated with apolipoprotein E genotype and trisomy 21 (Down syndrome).

The discovery that the epsilon 4 allele of the apolipoprotein E (apoE) gene is a putative risk factor for Alzheimer disease (AD) in the general population has highlighted the role of genetic influences in this extremely common and disabling illness. It has long been recognized that another genetic abnormality, trisomy 21 (Down syndrome), is associated with early and severe development of AD neuropathological lesions. It remains a challenge, however, to understand how these facts relate to the pathological changes in the brains of AD patients. We used computerized image analysis to examine the size distribution of one of the characteristic neuropathological lesions in AD, deposits of A beta peptide in senile plaques (SPs). Surprisingly, we find that a log-normal distribution fits the SP size distribution quite well, motivating a porous model of SP morphogenesis. We then analyzed SP size distribution curves in genotypically defined subgroups of AD patients. The data demonstrate that both apoE epsilon 4/AD and trisomy 21/AD lead to increased amyloid deposition, but by apparently different mechanisms. The size distribution curve is shifted toward larger plaques in trisomy 21/AD, probably reflecting increased A beta production. In apoE epsilon 4/AD, the size distribution is unchanged but the number of SP is increased compared to apoE epsilon 3, suggesting increased probability of SP initiation. These results demonstrate that subgroups of AD patients defined on the basis of molecular characteristics have quantitatively different neuropathological phenotypes.

Size distribution curves of senile plaques in patients with Alzheimer’s disease: do plaques grow according to the log-normal model?

The size frequency distributions of diffuse, primitive and cored senile plaques (SP) were studied in single sections of the temporal lobe from 10 patients with Alzheimer’s disease (AD). The size distribution curves were unimodal and positively skewed. The size distribution curve of the diffuse plaques was shifted towards larger plaques while those of the neuritic and cored plaques were shifted towards smaller plaques. The neuritic/diffuse plaque ratio was maximal in the 11 – 30 micron size class and the cored/ diffuse plaque ratio in the 21 – 30 micron size class. The size distribution curves of the three types of plaque deviated significantly from a log-normal distribution. Distributions expressed on a logarithmic scale were ‘leptokurtic’, i.e. with excess of observations near the mean. These results suggest that SP in AD grow to within a more restricted size range than predicted from a log-normal model. In addition, there appear to be differences in the patterns of growth of diffuse, primitive and cored plaques. If neuritic and cored plaques develop from earlier diffuse plaques, then smaller diffuse plaques are more likely to be converted to mature plaques.

The distribution of construction project bids

This paper describes an analysis of construction project bids to determine (a) the global distribution and (b) factors influencing the distribution of bids. The global distribution of bids was found, by using a battery of ll test statistics, to be approximated by a three-parameter log normal distribution. No global spread parameter was found. A multivariate analysis revealed the year of tender to be the major influencing factor. Consideration of the construction order, tender price and output indices lead to the conclusion that distributional spread reflected the degree of difference in pricing policies between bidders and the skewness of the distributions reflected the degree of competition. The paper concludes with a tentative model of the causal relationships between the factors and distributional characteristics involved.

Normal reference values of strength in pelvic floor muscle of women: A descriptive and inferential study

Background To describe the clinical, functional and quality of life characteristics in women with Stress Urinary Incontinence (SUI). In addition, to analyse the relationship between the variables reported by the patients and those informed by the clinicians, and the relationship between instrumented variables and the manual pelvic floor strength assessment. Methods Two hundred and eighteen women participated in this observational, analytical study. An interview about Urinary Incontinence and the quality of life questionnaires (EuroQoL-5D and SF-12) were developed as outcomes reported by the patients. Manual muscle testing and perineometry as outcomes informed by the clinician were assessed. Descriptive and correlation analysis were carried out. Results The average age of the subjects was (39.93?±?12.27 years), (24.49?±?3.54 BMI). The strength evaluated by manual testing of the right levator ani muscles was 7.79?±?2.88, the strength of left levator ani muscles was 7.51?±?2.91 and the strength assessed with the perineometer was 7.64?±?2.55. A positive correlation was found between manual muscle testing and perineometry of the pelvic floor muscles (p?normal distribution of a large sample of women with SUI was done, which provided the clinic with a baseline. There is a relationship between the strength of the pelvic muscles assessed manually and that obtained by a perineometer in women with SUI. There was no relationship between these values of strength and quality of life perceived.

Size-resolved particle distribution and gaseous concentrations by real-world road tunnel measurement

Measurements of aerosol particle number size distributions (15-700 nm), CO and NOx were performed in a bus tunnel, Australia. Daily mean particle size distributions of mixed diesel/CNG (Compressed Natural Gas) buses traffic flow were determined in 4 consecutive measurement days. EFs (Emission Factors) of Particle size distribution of diesel buses and CNG buses were obtained by MLR (Multiple Linear Regression) methods, particle distributions of diesel buses and CNG buses were observed as single accumulation mode and nuclei-mode separately. Particle size distributions of mixed traffic flow were decomposed by two log-normal fitting curves for each 30 minutes interval mean scans, all the mix fleet PSD emission can be well fitted by the summation of two log-normal distribution curves, and these were composed of nuclei mode curve and accumulation curve, which were affirmed as the CNG buses and diesel buses PN emission curves respectively. Finally, particle size distributions of diesel buses and CNG buses were quantified by statistical whisker-box charts. For log-normal particle size distribution of diesel buses, accumulation mode diameters were 74.5～87.5nm, geometric standard deviations were 1.89～1.98. As to log-normal particle size distribution of CNG buses, nuclei-mode diameters were 21～24 nm, geometric standard deviations were 1.27～1.31.

FIRST PASSAGE APPROXIMATION FOR NORMAL STATIONARY RANDOM PROCESSES.

A new approximate solution for the first passage probability of a stationary Gaussian random process is presented which is based on the estimation of the mean clump size. A simple expression for the mean clump size is derived in terms of the cumulative normal distribution function, which avoids the lengthy numerical integrations which are required by similar existing techniques. The method is applied to a linear oscillator and an ideal bandpass process and good agreement with published results is obtained. By making a slight modification to an existing analysis it is shown that a widely used empirical result for the asymptotic form of the first passage probability can be deduced theoretically.

Statistics of reaction progress variable and mixture fraction gradients from DNS of turbulent partially premixed flames

Statistically planar turbulent partially premixed flames for different initial intensities of decaying turbulence have been simulated for global equivalence ratios = 0.7 and 1.0 using three-dimensional, simplified chemistry-based direct numerical simulations (DNS). The simulation parameters are chosen such that the flames represent the thin reaction zones regime combustion. A random bimodal distribution of equivalence ratio is introduced in the unburned gas ahead of the flame to account for the mixture inhomogeneity. The results suggest that the probability density functions (PDFs) of the mixture fraction gradient magnitude |Δξ| (i.e., P(|Δξ|)) can be reasonably approximated using a log-normal distribution. However, this presumed PDF distribution captures only the qualitative nature of the PDF of the reaction progress variable gradient magnitude |Δc| (i.e., P(|Δc|)). It has been found that a bivariate log-normal distribution does not sufficiently capture the quantitative behavior of the joint PDF of |Δξ| and |Δc| (i.e., P(|Δξ|, |Δc|)), and the agreement with the DNS data has been found to be poor in certain regions of the flame brush, particularly toward the burned gas side of the flame brush. Moreover, the variables |Δξ| and |Δc| show appreciable correlation toward the burned gas side of the flame brush. These findings are corroborated further using a DNS data of a lifted jet flame to study the flame geometry dependence of these statistics. © 2013 Copyright Taylor and Francis Group, LLC.

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

The Effect of Volume Shape Factor on the Crystal Size Distribution of Fragments due to Attrition

The effect of volume shape factor on crystal size distribution (CSD) is usually ignored to simplify the analysis of population balance equation. In the present work, the CSD of fragments generated from a mechanically stirred crystallizer as the result of attrition mechanism has been reported when the volume shape factor conforms to normal distribution. The physical model of GAHN and MERSMANN which relates the attrition resistance of a crystalline substances to its mechanical properties has been employed. The simulation of fragment size distribution was performed by Monte Carlo (MC) technique. The results are compared with those reported by GAHN and MERSMANN.

On the Assumption of Bivariate Normality in Selection Models: A Copula Approach Applied to Estimating HIV Prevalence

Background: Heckman-type selection models have been used to control HIV prevalence estimates for selection bias when participation in HIV testing and HIV status are associated after controlling for observed variables. These models typically rely on the strong assumption that the error terms in the participation and the outcome equations that comprise the model are distributed as bivariate normal.
Methods: We introduce a novel approach for relaxing the bivariate normality assumption in selection models using copula functions. We apply this method to estimating HIV prevalence and new confidence intervals (CI) in the 2007 Zambia Demographic and Health Survey (DHS) by using interviewer identity as the selection variable that predicts participation (consent to test) but not the outcome (HIV status).
Results: We show in a simulation study that selection models can generate biased results when the bivariate normality assumption is violated. In the 2007 Zambia DHS, HIV prevalence estimates are similar irrespective of the structure of the association assumed between participation and outcome. For men, we estimate a population HIV prevalence of 21% (95% CI = 16%–25%) compared with 12% (11%–13%) among those who consented to be tested; for women, the corresponding figures are 19% (13%–24%) and 16% (15%–17%).
Conclusions: Copula approaches to Heckman-type selection models are a useful addition to the methodological toolkit of HIV epidemiology and of epidemiology in general. We develop the use of this approach to systematically evaluate the robustness of HIV prevalence estimates based on selection models, both empirically and in a simulation study.