scholarly journals A note on the relations of certain parameters following a logarithmic transformation

1955 ◽  
Vol 34 (2) ◽  
pp. 289-296 ◽  
Author(s):  
Mary Bagenal
Keyword(s):  
Coefficient Of Variation ◽  
Biological Data ◽  
Logarithmic Transformation ◽  
Confidence Limits ◽  
Formal Relation ◽  
Log Normal ◽  
Constant Coefficient Of Variation ◽  
Log Normal Distribution ◽  
Different Sources

The logarithmic transformation has been used in the statistical analysis of certain marine biological data. Parameters calculated from the transformed distributions have been used in the description of the observations, but it appears that some of the mathematical procedures adopted have not been fully understood.Winsor & Clarke (1940) have analysed data from plankton hauls. The problem considered by them was the determination of the variability in numbers of animals caught by repeated hauls through the same body of water. The raw data were characterized by a constant coefficient of variation, i.e. the variability in catch was proportional to the size of the catch. By transformation from the actual numbers caught to their logarithmic values, it was possible to equalize the variances and to apply the method of analysis of variance to esti-mate the variability due to the different sources. Finally, an estimate of the coefficient of variation was obtained from the logarithmic values. Their method of estimation was quoted by Snedecor (1946, p. 451) and was employed by Barnes & Bagenal (1951) in their study of repeated trawl hauls. Barnes & Bagenal also calculated confidence limits for comparison of observations following the method of Silliman (1946) in his work on pilchard eggs. These methods seem to be based on a misunderstanding of the nature of a trans-formation. The formal relation between the variance of such transformed data and the coefficient of variation of the untransformed data follows from the moments of the ‘log-normal’ distribution, given first by Wicksell (1917). From these moments it will be shown that the method given by Winsor & Clarke is mathematically unsound.

scholarly journals Water sensitive papers simulation to assess deposits on targets

2013 ◽  
Vol 44 (2s) ◽  
Author(s):  
Emanuele Cerruto ◽  
Claudia Aglieco
Keyword(s):  
Image Data ◽  
Phytosanitary Treatment ◽  
Processing Software ◽  
Image Processing Software ◽  
Log Normal ◽  
Constant Coefficient Of Variation ◽  
The Impact ◽  
Log Normal Distribution ◽  
Effective Water

Aim of the study is to assess the possibility to use water sensitive papers to estimate, beside the superficial coverage, also the amount of deposit on the target at varying the spray features. To point out the main quantities influencing the deposit, the behaviour of the water sensitive papers was simulated by assuming some simplifying hypotheses: log-normal distribution of the diameter population of the drops and circular spots. Several images (630) of water sensitive papers, sprayed with drops of different mean diameter (from 100 up to 500 μm), constant coefficient of variation (0.50), and theoretical percentage of covered surface ranging from 10 up to 100%, were produced by means of simulation. These images were considered as effective water sensitive paper images and then analysed by means of an image processing software. The correlations between measured and effective values were studied and they allowed for an estimate of deposit and spray features from the image data. This implies that the analysis of the water sensitive paper images allows the determination of more complex parameters such as the unitary deposit and the impact density, all data strictly related to the efficacy of a phytosanitary treatment.

Determination of Particle Size of a Dispersed Phase by Small-Angle X-ray Scattering

1989 ◽  
Vol 171 ◽  
Author(s):  
Frank C. Wilson
Keyword(s):  
Particle Size ◽  
High Resolution ◽  
Spherical Particles ◽  
Dispersed Phase ◽  
X Ray ◽  
X Ray Scattering ◽  
Resultant Data ◽  
Log Normal ◽  
Log Normal Distribution

ABSTRACTA method for determining particle diameters up to ca 500 rnm is described. X-ray data are obtained with an ultra-high resolution Bonse-Hart diffractometer and subsequently desmeared. The resultant data, viewed as the invariant argument h l(h), are interpreted as arising from a log-normal distribution of independent spherical particles. The distribution is characterized by its median value and breadth.

SERUM THYROGLOBULIN IN PATIENTS WITH TOXIC AND NON-TOXIC GOITRES COMPARED TO SEX- AND AGE-MATCHED CONTROL SUBJECTS

1979 ◽  
Vol 91 (2) ◽  
pp. 264-270 ◽  
Author(s):  
Ulla Feldt-Rasmussen ◽  
Karine Bech ◽  
John Date
Keyword(s):  
Matched Control ◽  
Diagnostic Value ◽  
Thyroid Disorders ◽  
Serum Thyroglobulin ◽  
Control Subjects ◽  
Distribution Of Values ◽  
Log Normal ◽  
Log Normal Distribution ◽  
Serum Tsh

ABSTRACT To study serum thyroglobulin (Tg) levels in patients with thyroid disorders compared to sex- and age-matched control subjects and to correlate the Tg levels to the thyroid function, 71 patients were investigated before treatment was started. Serum Tg, measured by a double antibody radioimmunoassay, was elevated in all groups with thyroid disorders, as compared to their controls, but the values showed large overlaps between groups. The highest median values were seen in the two groups of patients with toxic goitres (toxic adenoma and Graves' disease). The Tg values in patients with non-toxic goitres (diffuse and nodular) and in controls showed a log normal distribution, whereas the distribution of values from patients with toxic goitres was different. No correlation was found between serum Tg and serum thyroxine, serum triiodothyronine and serum TSH, respectively. It is concluded that determination of serum Tg is of little diagnostic value in thyroid diseases.

scholarly journals EXTRACTION, HYDROLYSIS, AND ELECTROPHORETIC ANALYSIS OF RIBONUCLEIC ACID FROM MICROSCOPIC TISSUE UNITS (MICROPHORESIS)

1960 ◽  
Vol 8 (1) ◽  
pp. 39-46 ◽  
Author(s):  
Jan-Erik Edström
Keyword(s):  
Quantitative Determination ◽  
Ultraviolet Light ◽  
Coefficient Of Variation ◽  
Ribonucleic Acid ◽  
Single Cells ◽  
Electrophoretic Analysis ◽  
Test Substance ◽  
Different Sources ◽  
Purine Pyrimidine

A procedure for the purine-pyrimidine analysis of RNA in the 100- to 1000 µµg. range is presented. It includes hydrolysis and electrophoretic analysis of RNA, which is extracted from single isolated tissue units, like single cells. The quantitative determination of the separated compounds is carried out by a photographic-photometric procedure in ultraviolet light. The determined values show a coefficient of variation of about ±7 per cent on test substance. Microelectrophoretic analyses of RNA from different sources have been performed and are compared to macrochemical analyses. The agreement is good in those cases in which it is possible to get any information at all through macrochemical analyses.

scholarly journals The Generalized DUS Transformed Log-Normal Distribution and Its Applications to Cancer and Heart Transplant Datasets

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3113
Author(s):  
Muhammed Rasheed Irshad ◽  
Christophe Chesneau ◽  
Soman Latha Nitin ◽  
Damodaran Santhamani Shibu ◽  
Radhakumari Maya
Keyword(s):  
Maximum Likelihood ◽  
Normal Distribution ◽  
Hazard Rate ◽  
Rate Function ◽  
Biological Data ◽  
Hazard Rate Function ◽  
Bayesian Techniques ◽  
Log Normal ◽  
Log Normal Distribution ◽  
New Distribution

Many studies have underlined the importance of the log-normal distribution in the modeling of phenomena occurring in biology. With this in mind, in this article we offer a new and motivated transformed version of the log-normal distribution, primarily for use with biological data. The hazard rate function, quantile function, and several other significant aspects of the new distribution are investigated. In particular, we show that the hazard rate function has increasing, decreasing, bathtub, and upside-down bathtub shapes. The maximum likelihood and Bayesian techniques are both used to estimate unknown parameters. Based on the proposed distribution, we also present a parametric regression model and a Bayesian regression approach. As an assessment of the longstanding performance, simulation studies based on maximum likelihood and Bayesian techniques of estimation procedures are also conducted. Two real datasets are used to demonstrate the applicability of the new distribution. The efficiency of the third parameter in the new model is tested by utilizing the likelihood ratio test. Furthermore, the parametric bootstrap approach is used to determine the effectiveness of the suggested model for the datasets.

Analysis of Tritium in Water: A Collaborative Study

1969 ◽  
Vol 52 (1) ◽  
pp. 90-93
Author(s):  
Vincent J Sodd ◽  
Kenneth L Scholz
Keyword(s):  
Systematic Error ◽  
Coefficient Of Variation ◽  
Liquid Scintillation ◽  
Collaborative Study ◽  
Minimum Detectable Activity ◽  
Confidence Limits ◽  
Detectable Activity ◽  
Counting Time ◽  
Statistical Results

Abstract A liquid scintillation procedure using 1,4-dioxane, naphthalene, PPO, and POPOP as the scintillator was evaluated in a collaborative study of the determination of tritium in water. The tritium counting efficiencies for seven collaborating laboratories using this technique and commercially available liquid scintillation spectrometers ranged from 8.3 to 26.5%. The minimum detectable activity by the method, based on 99% confidence limits, 100 min counting time, and backgrounds from 9 to 67 cpm, ranged from 0.2 to 0.5 pCi/ml. Statistical results showed no evidence for systematic error. The coefficient of variation varies from 3.4 to 7.3% over the concentration range 2.91–115.8 pCi/ml. It is recommended that the method be adopted as official first action.

scholarly journals Development of the New Analytic Model for Sand Deposition Particles Downstream of a Fence

Inventions ◽  
2020 ◽  
Vol 5 (1) ◽  
pp. 4
Author(s):  
Peyman Razi
Keyword(s):  
Snow Accumulation ◽  
Analytic Model ◽  
Distribution Profile ◽  
Proposed Model ◽  
Simulation Domain ◽  
Discrete Phase ◽  
Sand Particles ◽  
Log Normal ◽  
Log Normal Distribution

Movement of sand particles is a complicated phenomenon that occurs in nature. In this paper, the main goal is to provide an analytic model for the deposition profile of sand particles downstream of a fence. The analytic model was derived with respect to governing equations and shear flows for upstream and downstream regions. In this approach, we obtain a new expression for the downstream velocity of the fence, which allows for the determination of potential areas of deposition particles by assuming a log-normal distribution profile. A discrete-phase flow (DPM) was used to inject particles in the simulation domain. The DPM gives capabilities to capture spatiotemporal velocities components, as we can define the probability of deposition particles in the downstream of the fence. The proposed model was validated with a numerical model and experimental results. The comparison with field data and numerical results shows that the deposition profile is in acceptable agreement. With some assumptions and modifications about the properties of particles, the results of this research can be extended to snow accumulation downstream of a fence.

Distribution of Eyeblink Amplitude Recorded by an Electrode Hookup: Re-Examination

1980 ◽  
Vol 51 (3_suppl2) ◽  
pp. 1283-1287 ◽  
Author(s):  
Fumio Yamada ◽  
Katsuyuki Yamasaki ◽  
Makoto Nakayama ◽  
Yo Miyata
Keyword(s):  
White Noise ◽  
Normal Distribution ◽  
Present Experiment ◽  
Logarithmic Transformation ◽  
Startle Eyeblink ◽  
Distributional Properties ◽  
Distribution Property ◽  
Log Normal ◽  
Log Normal Distribution

The present experiment was run to re-examine the distributional properties of the eyeblink amplitude elicited by a burst of 110-dB white noise, recorded by an electrode hookup as recommended in our previous report (Yamada, Yamasaki, & Miyata, 1979). 103 volunteers, 54 males and 49 females, were tested. Analysis showed that the amplitudes were distributed normally when a logarithmic transformation was performed but not when the raw scores were used. We conclude that the amplitude of the startle eyeblink reflex has a log-normal distribution property.

Determination of particle size distribution in an Fe2O3-based catalyst using magnetometry and x-ray diffraction

1992 ◽  
Vol 7 (7) ◽  
pp. 1856-1860 ◽  
Author(s):  
Manjula M. Ibrahim ◽  
Jianmin Zhao ◽  
Mohindar S. Seehra
Keyword(s):  
Particle Size ◽  
Particle Size Distribution ◽  
Size Distribution ◽  
Line Broadening ◽  
X Ray Diffraction ◽  
X Ray ◽  
Mössbauer Measurements ◽  
Log Normal ◽  
Log Normal Distribution

In this paper, the techniques of SQUID magnetometry and line broadening in x-ray diffraction are employed for determining an important parameter for catalysts, viz. the particle size distribution. Magnetization versus temperature (5 K–400 K) and magnetization versus field (up to 55 kOe) data are reported for an α–Fe2O3 based catalyst. After determining the region of superparamagnetism, the distribution function f(r) is determined assuming a log normal distribution and Langevin paramagnetism of superparamagnetic particles. The distribution is found to be fairly symmetric with center near 65 Å and range of 35 to 115 Å. From line-broadening of Bragg peaks in x-ray diffraction, particle radii varying between 75 Å and 110 Å are obtained. These results are compared with the reported Mössbauer measurements of Huffman et al. on the same sample.

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