Truncated Log-Normal and Root-Normal Frequency Distributions of Insect Populations

Nature ◽  
1948 ◽  
Vol 162 (4118) ◽  
pp. 530-531 ◽  
Author(s):  
D. SPILLER
Keyword(s):  
Frequency Distributions ◽  
Normal Frequency ◽  
Insect Populations ◽  
Log Normal

Homeokinesis and short-term variability of human airway caliber

2001 ◽  
Vol 91 (3) ◽  
pp. 1131-1141 ◽  
Author(s):  
Cheng-Li Que ◽  
C. M. Kenyon ◽  
R. Olivenstein ◽  
Peter T. Macklem ◽  
Geoffrey N. Maksym
Keyword(s):  
Supine Position ◽  
Normal Subjects ◽  
Forced Oscillations ◽  
Short Term ◽  
Frequency Distributions ◽  
Airway Narrowing ◽  
Asthmatic Patients ◽  
Airway Caliber ◽  
Normal Frequency ◽  
Log Normal

We hypothesized that short-term variation in airway caliber could be quantified by frequency distributions of respiratory impedance (Zrs) measured at high frequency. We measured Zrs at 6 Hz by forced oscillations during quiet breathing for 15 min in 10 seated asthmatic patients and 6 normal subjects in upright and supine positions before and after methacholine (MCh). We plotted frequency distributions of Zrs and calculated means, skewness, kurtosis, and significance of differences between normal and log-normal frequency distributions. The data were close to, but usually significantly different from, a log-normal frequency distribution. Mean lnZrs in upright and supine positions was significantly less in normal subjects than in asthmatic patients, but not after MCh and MCh in the supine position. The lnZrs SD (a measure of variation), in the upright position and after MCh was significantly less in normal subjects than in asthmatic patients, but not in normal subjects in the supine position and after MCh in the supine position. We conclude that 1) the configuration of the normal tracheobronchial tree is continuously changing and that this change is exaggerated in asthma, 2) in normal lungs, control of airway caliber is homeokinetic, maintaining variation within acceptable limits, 3) normal airway smooth muscle (ASM) when activated and unloaded closely mimics asthmatic ASM, 4) in asthma, generalized airway narrowing results primarily from ASM activation, whereas ASM unloading by increasing shortening velocity allows faster caliber fluctuations, 5) activation moves ASM farther from thermodynamic equilibrium, and 6) asthma may be a low-entropy disease exhibiting not only generalized airway narrowing but also an increased appearance of statistically unlikely airway configurations.

scholarly journals Statistical distributions of water content and sizes for clouds above Europe

2000 ◽  
Vol 18 (3) ◽  
pp. 385-397 ◽  
Author(s):  
R. P. H. Berton
Keyword(s):  
Water Content ◽  
Critical Analysis ◽  
Cross Correlation ◽  
Correlation Coefficients ◽  
Original Data ◽  
Atmospheric Dynamics ◽  
Statistical Distributions ◽  
Frequency Distributions ◽  
Meteorology And Atmospheric Dynamics ◽  
Log Normal

Abstract. The statistics of quantities involved in the synthesis of cloud scenes have been investigated from an original data base. Frequency distributions of ice and water content (IWC), horizontal and vertical sizes (L and H), and top temperatures (T) of clouds above Europe have been derived for nine types of clouds (As, Cb, Ci, Cg, LwCg, OrCg, Cs, Ns, Sc). It appears that the cumulated frequency plots can be well fitted with log-normal or Weibull profiles, and that for IWC and T cloud types can be split into two or three classes according to slopes in logarithmic coordinates. Cross-correlation coefficients between IWC, L, H and T have been also derived. Implications for the physics of the cloud build-up processes are briefly outlined. Critical analysis and comparison of other published results are proposed.Key words: Meteorology and atmospheric dynamics (climatology)

Hydraulic conductivity of deeply weathered materials in the Darling Range, Western Australia

Soil Research ◽  
1980 ◽  
Vol 18 (2) ◽  
pp. 129 ◽  
Author(s):  
AJ Peck ◽  
PA Yendle ◽  
FE Batini
Keyword(s):  
Hydraulic Conductivity ◽  
Western Australia ◽  
Gaussian Function ◽  
Normal Function ◽  
Test Method ◽  
Poor Correlation ◽  
Frequency Distributions ◽  
Grid Points ◽  
Log Normal ◽  
Made In

The hydraulic conductivity (K) of unconsolidated, deeply weathered material was measured by the slug test method In 214 boreholes distributed over five distinct areas in the Darling Range of Western Australia. Most of the measurements were made in the zone 0-3 m above hard rock. Theory of the method was extended to include a layer of material with lower K about the slotted pipe. The frequency distribution of K in each area was well fitted by the log-normal function. Parameters of the linear regression of logK against the inverse Gaussian function of cumulative frequency differed significantly (P<0.001) between areas. In one area of 134 ha, measurements were made in 54 boreholes located on a grid. There was a very poor correlation between values of K at the smallest separation of grid points (100 m), which suggests that there is an essentially random spatial variation of K measured by this method in this study area. Assuming log-normal frequency distributions and random spatial distributions, bulk conductivities were estimated for each area. On the basis of these investigations, it is concluded that the bulk hydraulic conductivity of the weathered material in the Darling Range is slow to moderately slow, and relatively uniform on the broad scale.

Relations between abundance, body size and species number in British birds and mammals

1996 ◽  
Vol 351 (1337) ◽  
pp. 265-278 ◽  
Keyword(s):  
Body Size ◽  
Frequency Distribution ◽  
Body Mass ◽  
Species Number ◽  
Metabolic Rates ◽  
Frequency Distributions ◽  
Migrant Birds ◽  
Log Normal ◽  
Normally Distributed

British birds and mammals are compared in terms of their frequency distributions of abundance and body mass and in respect of the relation between abundance and body mass. Body masses of non-flying mammals are greater than those of resident birds which are, in turn, heavier than migrants; bats are lightest. The frequency distribution of masses are close to log-Normal for each of these groups, though their variances and skews differ. Differences in mean abundances (which are log-Normally distributed) parallel those in body mass. In each group, abundance declines with body mass: the exponent of the relation is close to the value of —0.75 predicted by the ‘energetic equivalence’ rule though not significantly different from the value of — 1.0 predicted by the ‘biomass equivalence’ rule. At comparable masses, species of non-flying mammals are more abundant than resident birds, migrant birds and bats by approximately 45, 300 and 200 times, respectively. The similarity between birds and bats in this regard may be no more than coincidental but it may be related to ecological similarities related to flight. The metabolic rates of non-flying mammals may be generally lower than those of birds and bats but not sufficiently to account for their much greater abundances.

scholarly journals On the identification of Dragon Kings among extreme-valued outliers

2013 ◽  
Vol 20 (4) ◽  
pp. 549-561 ◽  
Author(s):  
M. Riva ◽  
S. P. Neuman ◽  
A. Guadagnini
Keyword(s):  
Heavy Tails ◽  
Extreme Values ◽  
Statistical Tests ◽  
Synthetic Data ◽  
Gaussian Random Fields ◽  
Power Functions ◽  
Parent Population ◽  
Frequency Distributions ◽  
Black Swans ◽  
Log Normal

Abstract. Extreme values of earth, environmental, ecological, physical, biological, financial and other variables often form outliers to heavy tails of empirical frequency distributions. Quite commonly such tails are approximated by stretched exponential, log-normal or power functions. Recently there has been an interest in distinguishing between extreme-valued outliers that belong to the parent population of most data in a sample and those that do not. The first type, called Gray Swans by Nassim Nicholas Taleb (often confused in the literature with Taleb's totally unknowable Black Swans), is drawn from a known distribution of the tails which can thus be extrapolated beyond the range of sampled values. However, the magnitudes and/or space–time locations of unsampled Gray Swans cannot be foretold. The second type of extreme-valued outliers, termed Dragon Kings by Didier Sornette, may in his view be sometimes predicted based on how other data in the sample behave. This intriguing prospect has recently motivated some authors to propose statistical tests capable of identifying Dragon Kings in a given random sample. Here we apply three such tests to log air permeability data measured on the faces of a Berea sandstone block and to synthetic data generated in a manner statistically consistent with these measurements. We interpret the measurements to be, and generate synthetic data that are, samples from α-stable sub-Gaussian random fields subordinated to truncated fractional Gaussian noise (tfGn). All these data have frequency distributions characterized by power-law tails with extreme-valued outliers about the tail edges.

Loss and induction of conditional dormancy in seeds of Sitka spruce maintained moist at different temperatures

1997 ◽  
Vol 7 (4) ◽  
pp. 351-358 ◽  
Author(s):  
Steve K. Jones ◽  
Richard H. Ellis ◽  
Peter G. Gosling
Keyword(s):  
Seed Dormancy ◽  
Sitka Spruce ◽  
Picea Sitchensis ◽  
Frequency Distributions ◽  
C Cycle ◽  
Normal Frequency ◽  
Different Temperatures ◽  
Pretreatment Temperature ◽  
Logarithmic Relationship ◽  
Multiplicative Models

AbstractPretreatment of moist seeds at certain temperatures can reduce seed dormancy, but such observations represent the net effect of pretreatment. Seeds of Sitka spruce (Picea sitchensis [Bong.] Carr.) were raised to 30% moisture content and pretreated at five different temperatures between 5 and 30°C for up to 24 weeks (168 d). Subsequent ability to germinate at 10°C and viability were then determined in order to investigate the effects of pretreatment on seed dormancy and survival. There was a curvilinear, negative semi-logarithmic relationship between seed longevity and pretreatment temperature, such that Q10 for loss in viability increased from 2.6 between 10 and 20°C to 2.8 between 20 and 30°C. Simple multiplicative models combining cumulative normal frequency distributions for each of loss in viability and loss in dormancy were able to describe the changes in ability to germinate at 10°C, after pretreatment at 5, 10 and 30°C. However, in order to quantify the changes in ability to germinate observed at 10°C after pretreatment at 15°C, it was necessary also to invoke a model of dormancy reimposition, while for the results at 20°C it was necessary to postulate both dormancy reimposition and the further loss of this reimposed dormancy. It is concluded that moist seeds of Sitka spruce held at 15 and 20°C cycle between the dormant and non-dormant condition.

Distribution of Self-Reported Alcohol Consumption in New Zealand, 1978–1979

1980 ◽  
Vol 47 (1) ◽  
pp. 159-170 ◽  
Author(s):  
Robert A. M. Gregson ◽  
Barrie G. Stacey
Keyword(s):  
Time Series ◽  
New Zealand ◽  
Alcohol Consumption ◽  
Frequency Distribution ◽  
National Survey ◽  
Recent History ◽  
Normal Frequency ◽  
Total Alcohol ◽  
History Of ◽  
Log Normal

The problem of estimating how much alcohol individuals actually drink is discussed with particular reference to the log-normal frequency distribution of alcohol consumption. It is then presented as being a problem of inference from the recent history of a time series. Following directly from this presentation, data obtained in a national survey of 10,000 New Zealand residents are analyzed (a) to yield the frequency distribution of estimated drinking rates; (b) to test whether this distribution is log-normal in form; and (c) to provide further information about the distribution of alcohol consumption. This analysis enabled us to account for almost the whole of the actual total alcohol consumption in New Zealand. The results are different from those expected on the basis of the uncorrected log-normal description of consumption.

Is Alcohol Consumption Log-Normally Distributed among Fourteen- to Seventeen-Year-Olds?

1981 ◽  
Vol 48 (3) ◽  
pp. 995-1005 ◽  
Author(s):  
Barrie G. Stacey ◽  
Geoffrey A. Elvy
Keyword(s):  
New Zealand ◽  
Alcohol Consumption ◽  
Total Sample ◽  
Normal Distributions ◽  
Theoretical Position ◽  
High Consumption ◽  
Normal Frequency ◽  
Log Normal ◽  
Nation Wide Survey ◽  
Log Normal Distribution

The problem of explaining the distribution of alcohol consumption in a population is discussed with particular reference to the log-normal frequency distribution of alcohol consumption and the claims associated with it. Criticisms directed at this application of the log-normal distribution are presented, as is Ole-Jørgen Skog's defense of the log-normal hypothesis. A nation-wide survey of alcohol consumption by 1278 New Zealand 14- to 17-yr.-olds is described. In this sample, representing homogeneous substrata of the New Zealand population, the distribution of alcohol consumption is not close to log-normality in the high consumption segment of the distribution for males, females, and the total sample. However, some analysts would probably interpret our results as borderline or even approximate log-normal distributions. The significance of these results for the log-normal hypothesis and Skog's theoretical position is outlined. Important features of alcohol consumption among 14- to 17-yr.-olds in New Zealand are discussed.

ESTABLISHMENT OF THE MODAL PROFILE AND MEASUREMENT OF VARIABILITY WITHIN A SOIL LANDFORM UNIT

1968 ◽  
Vol 48 (1) ◽  
pp. 7-19 ◽  
Author(s):  
R. Protz ◽  
E. W. Presant ◽  
R. W. Arnold
Keyword(s):  
Basic Data ◽  
Soil Profiles ◽  
Frequency Distributions ◽  
Normal Distributions ◽  
Landform Unit ◽  
Normal Frequency ◽  
Mapping Units

A method for establishing a modal profile and separating inclusions in mapping units is presented. The statistical concepts and implications are discussed. Horizon thicknesses of 100 soil profiles in a 10-by-10 grid on a stable, remnant, upland terrace were used as the basic data to demonstrate the method. All horizon thicknesses did not follow normal frequency distributions, the Ae and AB were skewed and the depth to carbonates exhibited a tendency to a bi-modal distribution, whereas the Ah and B horizons approached normal distributions.

Frequency distributions of parasites in a population of three-spined sticklebacks, Gasterosteus aculeatus L., with particular reference to the negative binomial distribution

Parasitology ◽  
1971 ◽  
Vol 63 (3) ◽  
pp. 389-406 ◽  
Author(s):  
Linda Pennycuick
Keyword(s):  
Gasterosteus Aculeatus ◽  
Negative Binomial ◽  
Science Research ◽  
Life Cycles ◽  
Frequency Distributions ◽  
Original Distribution ◽  
Log Normal ◽  
University Of Bristol ◽  
Host Parasite ◽  
Parasite Populations

All three species of parasites found in sticklebacks from Priddy had overdispersed distributions, similar in shape to host–parasite distributions described by other authors.The distributions of both Echinorhynchus clavula and Diplostomum gasterostei were fitted closely by the negative binomial. The values of k were similar for both species, being always less than unity; the Diplostomum distributions were more overdispersed and therefore had higher values of p.The Schistocephalus distributions were mostly described by the log normal, but the high percentage infection and relatively low overdispersion meant that the fit was often not close. There was also some truncation at the upper end.The relationship between the parameters of the negative binomial (p and k) and the shape and parameters of the original distribution have been investigated, both theoretically and with respect to the distributions of the stickleback parasites.In general p varied as the overdispersion and k as the percentage infection.The advantages of an overdispersed distribution to the host and parasite populations are discussed and related to the life cycles of the parasites.I am most grateful to Dr H. D. Crofton for his help and encouragement during this study, and to the staff of the Computer Unit, University of Bristol for their assistance with programming problems. This work was supported by a Science Research Council research studentship and a NATO studentship.

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