scholarly journals Estimating the mean and variance from the five-number summary of a log-normal distribution

2020 ◽  
Vol 13 (4) ◽  
pp. 519-531
Author(s):  
Jiandong Shi ◽  
Tiejun Tong ◽  
Yuedong Wang ◽  
Marc G. Genton
Keyword(s):  
Normal Distribution ◽  
Mean And Variance ◽  
The Mean ◽  
Log Normal ◽  
Log Normal Distribution

scholarly journals Divergent estimates of ratio between Na+-Ca2+ current densities in t-tubular and surface membranes of rat cardiomyocytes

2021 ◽  
Author(s):  
Michal Pásek ◽  
Jiří Šimurda ◽  
Markéta Bébarová ◽  
Georges Christé
Keyword(s):  
Normal Distribution ◽  
Measured Data ◽  
Asymmetric Distribution ◽  
Rat Cardiomyocytes ◽  
Adult Rat ◽  
Current Densities ◽  
The Mean ◽  
Log Normal ◽  
Reported Data ◽  
Log Normal Distribution

The ratio between Na+-Ca2+ exchange current densities in t-tubular and surface membranes of rat ventricular cardiomyocytes (JNaCa-ratio) estimated from electrophysiological data published to date yields strikingly different values between 1.7 and nearly 40. Possible reasons of such divergence were analysed by Monte-Carlo simulations assuming either normal or log-normal distribution of measured data. The confidence intervals CI95 of the mean JNaCa-ratios computed from the reported data showed an overlap of values between 1 and 3 and between 0.3 and 4.3 in the case of normal and log-normal distribution, respectively. Further analysis revealed that the high published values likely result from a large scatter of data due to transmural differences in JNaCa, dispersion of cell membrane capacitances and variability in incomplete detubulation. Taking into account the asymmetric distribution of measured data, reduction of mean current densities after detubulation, and substantially smaller CI95 of lower values of the mean JNaCa-ratio, the values between 1.6 and 3.2 may be considered as the most accurate estimates. This implicates that 40 to 60% of Na+-Ca2+ exchanger is located at the t-tubular membrane of adult rat cardiomyocytes.

X-ray particle-size broadening

1986 ◽  
Vol 42 (1) ◽  
pp. 6-13 ◽  
Author(s):  
S. Rao ◽  
C. R. Houska
Keyword(s):  
Particle Size ◽  
Normal Distribution ◽  
Variation Coefficient ◽  
Column Height ◽  
X Ray Diffraction ◽  
Diffraction Profile ◽  
X Ray ◽  
The Mean ◽  
Log Normal ◽  
Log Normal Distribution

X-ray diffraction profiles and Fourier coefficients are given for particles distributed according to experimentally verified size distributions. Calculations are based upon the log normal distribution of sphere diameters and intercept lengths in addition to a normal distribution of column heights. It is found that the diffraction profile is not sensitive to the fine details of the distribution but rather the mean column height and the column-height variation coefficient. Errors in particle-size determinations will result from an improper choice of the variation coefficient. Two simplified models are given that describe the diffraction profiles for a large range of variation coefficients.

A Large Scale Fatigue Test of Aluminium Specimens

1965 ◽  
Vol 16 (4) ◽  
pp. 307-322 ◽  
Author(s):  
N. T. Bloomer ◽  
T. F. Roylance
Keyword(s):  
Distribution Function ◽  
Probability Distribution ◽  
Normal Distribution ◽  
Probability Of Failure ◽  
Distribution Functions ◽  
Experimental Results ◽  
Normal Distribution Function ◽  
The Mean ◽  
Log Normal ◽  
Log Normal Distribution

SummaryThere have been, in the past, many fatigue tests carried out on a variety of materials and components. These all indicate a wide scattering in the lives (measured by the number of stress cycles to failure) endured by nominally identical components subjected to nominally identical forces before failure occurs. To interpet this scattering several equations have been suggested as representing the statistical distribution functions that fit the lives obtained for individual types of component. Of these functions the log normal distribution function has been perhaps the most widely used. For the central regions of the probability distribution, i.e. about the mean, the log normal distribution and several others represent experimental results very closely indeed, but engineers and designers of all kinds dare not design on the mean fatigue life. They are concerned with specifications that either exclude the possibility of failure or admit only a very small probability of failure. It is thus with the accuracy with which the “lower tail” of the probability distribution curve fits the experimental results that they are concerned.To assess the fit at this lower end for one type of component, a large number (about 1,000) of aluminium specimens have been tested and the corresponding lives plotted. The results are very interesting. They show clearly that the log normal distribution for this type of component and material is pessimistic for a probability of failure of less than 0·3. This result is felt by the authors to be of very great importance. It has further been shown that the use of the “one-sided censored distribution function”, used previously by one of the authors, gives a curve that will fit the lower results better than the complete log normal distribution would do.It is with the testing procedure adopted, the specimens used, the distribution functions considered and the conclusions obtained therefrom that this paper is concerned.

scholarly journals A Universal Model for the Log-Normal Distribution of Elasticity in Polymeric Gels and Its Relevance to Mechanical Signature of Biological Tissues

Biology ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 64
Author(s):  
Arnaud Millet
Keyword(s):  
Elastic Modulus ◽  
Normal Distribution ◽  
Biological Tissues ◽  
Force Microscopy ◽  
Polymeric Gels ◽  
Atomic Force ◽  
Clear Explanation ◽  
Log Normal ◽  
Log Normal Distribution

The mechanosensitivity of cells has recently been identified as a process that could greatly influence a cell’s fate. To understand the interaction between cells and their surrounding extracellular matrix, the characterization of the mechanical properties of natural polymeric gels is needed. Atomic force microscopy (AFM) is one of the leading tools used to characterize mechanically biological tissues. It appears that the elasticity (elastic modulus) values obtained by AFM presents a log-normal distribution. Despite its ubiquity, the log-normal distribution concerning the elastic modulus of biological tissues does not have a clear explanation. In this paper, we propose a physical mechanism based on the weak universality of critical exponents in the percolation process leading to gelation. Following this, we discuss the relevance of this model for mechanical signatures of biological tissues.

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