scholarly journals Lorenz and Polarization Orderings of the Double-Pareto Lognormal Distribution and Other Size Distributions

Sankhya B ◽  
2021 ◽  
Author(s):  
Masato Okamoto
Keyword(s):  
Income Distribution ◽  
Lognormal Distribution ◽  
Sensitivity Analyses ◽  
Stochastic Orders ◽  
Size Distributions ◽  
Lorenz Order

AbstractPolarization indices such as the Foster-Wolfson index have been developed to measure the extent of clustering in a few classes with wide gaps between them in terms of income distribution. However, Zhang and Kanbur (2001) failed to empirically find clear differences between polarization and inequality indices in the measurement of intertemporal distributional changes. This paper addresses this ‘distinction' problem on the level of the respective underlying stochastic orders, the polarization order (PO) in distributions divided into two nonoverlapping classes and the Lorenz order (LO) of inequality in distributions. More specifically, this paper investigates whether a distribution F can be either more or less polarized than a distribution H in terms of the PO if F is more unequal than H in terms of the LO. Furthermore, this paper derives conditions for the LO and PO of the double-Pareto lognormal (dPLN) distribution. The derived conditions are applicable to sensitivity analyses of inequality and polarization indices with respect to distributional changes. From this application, a suggestion for appropriate two-class polarization indices is made.

Comparing Three Environmental Particle Size Distributions: Power Law (FED-STD-209D), Lognormal, Approximate Lognormal (MIL-STD-1246B)

1991 ◽  
Vol 34 (1) ◽  
pp. 21-24
Author(s):  
Douglas Cooper
Keyword(s):  
Particle Size ◽  
Power Law ◽  
Lognormal Distribution ◽  
Cumulative Distribution ◽  
Size Distributions ◽  
Power Law Distribution ◽  
Particle Size Distributions ◽  
Contamination Control ◽  
Control Programs ◽  
Power Law Distributions

Particle size strongly influences particle behavior. To summarize the distribution of particle sizes, a distribution function can be used. The characteristics of the particle size distributions chosen are important for two specification documents currently under revision: (1) FED-STD-209D, concerning air-cleanliness in manufacturing, which uses cumulative particle size distributions that are linear when plotted on log-log axes; these are power law distributions. (2) MIL-STD-1246B, "Product Cleanliness Levels and Contamination Control Programs," primarily concerning surface cleanliness, which uses cumulative particle size distributions that are linear when plotted as the logarithm of the cumulative distribution versus the square of the logarithm of the particle size, log2x, A third distribution, the lognormal, is commonly found in aerosol science, especially where there is a single particle source. The distributions are compared and discussed. The FED-STD-209D power law distribution can approximate a lognormal distribution over only a limited size range. The MIL-STD-1246B distribution is an asymptotic approximation to the lognormal distribution.

FROM LOGNORMAL DISTRIBUTION TO POWER LAW: A NEW CLASSIFICATION OF THE SIZE DISTRIBUTIONS

2006 ◽  
Vol 17 (10) ◽  
pp. 1429-1436 ◽  
Author(s):  
LUCIEN BENGUIGUI ◽  
EFRAT BLUMENFELD-LIEBERTHAL
Keyword(s):  
Normal Distribution ◽  
Power Law ◽  
Lognormal Distribution ◽  
Size Distributions ◽  
New Classification ◽  
Multiplicative Process ◽  
Random Multiplicative Process ◽  
Log Normal ◽  
Log Normal Distribution

We propose a new classification of the size distributions of entities based on an exponent α defined from the shape of the log–log Rank Size plot. From an inspection of a large number of cases in different fields, one finds three possibilities: α = 1 giving a power law, α > 1 (parabola like curve) and 0 < α < 1 (analogous to a log normal distribution). A fourth possibility that can be defined when α < 0 was never observed. We present a modified version of models based on a random multiplicative process and an introduction of new entities during the growth. We recover all three kinds of distributions and show that the type of a distribution is conditioned by the rate of the introduction of new entities.

scholarly journals The effects of neighbourhood and workplace income comparisons on subjective wellbeing

2021 ◽  
Author(s):  
◽  
Shakked Noy
Keyword(s):  
Income Distribution ◽  
Subjective Wellbeing ◽  
Causal Effect ◽  
Peer Groups ◽  
Sensitivity Analyses ◽  
Group Level ◽  
Mass Layoffs ◽  
Fairness Concerns ◽  
Linear Regressions ◽  
Over Time

<p>We investigate how the incomes of a person’s neighbours and coworkers affect her happiness, using survey data on subjective wellbeing linked to unprecedentedly rich administrative data on the characteristics of survey respondents’ peer groups. Linear regressions of subjective wellbeing on peer income variables establish that people care exclusively about their ordinal rank within their peer income distribution, that workplace rank matters much more than neighbourhood rank, and that workplace comparisons are driven primarily by fairness concerns. We confirm that our results reflect a causal effect of peer income by implementing sensitivity analyses, identifying off changes in peer income over time for immobile people, exploiting plausibly exogenous moves between workplaces triggered by mass layoffs, and testing for the effects of unobservable group-level confounders.</p>

Description of Atmospheric Aerosol Dynamics Using an Inverse Gaussian Distributed Method of Moments

2020 ◽  
Vol 77 (9) ◽  
pp. 3011-3031
Author(s):  
J. Shen ◽  
M. Yu ◽  
J. Lin
Keyword(s):  
Size Distribution ◽  
Method Of Moments ◽  
Lognormal Distribution ◽  
Atmospheric Aerosol ◽  
Aerosol Size Distribution ◽  
Geometric Standard Deviation ◽  
Test Cases ◽  
Size Distributions ◽  
Inverse Gaussian ◽  
Aerosol Dynamics

Abstract For nearly 60 years, the lognormal distribution has been the most widely used function in the field of atmospheric science for characterizing atmospheric aerosol size distribution. We verify whether the three-parameter inverse Gaussian distribution (IGD) is a more suitable function than the lognormal distribution for characterizing aerosol size distribution. An attractive feature of IGD is that with it a new method of moments (MOM) can be established for resolving atmospheric aerosol dynamics which is described by a kinetic aerosol dynamics equation, i.e., inverse Gaussian distributed MOM (IGDMOM). The advantage of IGDMOM is that all of its moments can be analytically calculated using a closure moment function inherited from IGD. The precision and efficiency of IGDMOM are verified by comparing it with other recognizable methods in test cases of four representative atmospheric aerosol dynamics. Several key statistical quantities determining aerosol size distributions, including kth moments (k = 0, 1/3, 2/3, and 2), geometric standard deviation, skewness, and kurtosis, are evaluated. IGDMOM has higher precision than the lognormal MOM with nearly identical efficiency. The article provides a novel alternative to atmospheric scientists for solving kinetic aerosol dynamics equations.

scholarly journals Modelling and measurements of urban aerosol processes on the neighborhood scale in Rotterdam, Oslo and Helsinki

2015 ◽  
Vol 15 (23) ◽  
pp. 35157-35200
Author(s):  
M. Karl ◽  
J. Kukkonen ◽  
M. P. Keuken ◽  
S. Lützenkirchen ◽  
L. Pirjola ◽  
...  
Keyword(s):  
Particle Size ◽  
Gas Phase ◽  
Dry Deposition ◽  
Particle Number ◽  
Measured Data ◽  
Sensitivity Analyses ◽  
Size Distributions ◽  
Particle Size Distributions ◽  
Coagulation Of Particles ◽  
Neighborhood Scale

Abstract. This study evaluates the influence of aerosol processes on the particle number (PN) concentrations in three major European cities on the temporal scale of one hour, i.e. on the neighborhood and city scales. We have used selected measured data of particle size distributions from previous campaigns in the cities of Helsinki, Oslo and Rotterdam. The aerosol transformation processes were evaluated using an aerosol dynamics model MAFOR, combined with a simplified treatment of roadside and urban atmospheric dispersion. We have compared the model predictions of particle number size distributions with the measured data, and conducted sensitivity analyses regarding the influence of various model input variables. We also present a simplified parameterization for aerosol processes, which is based on the more complex aerosol process computations; this simple model can easily be implemented to both Gaussian and Eulerian urban dispersion models. Aerosol processes considered in this study were (i) the coagulation of particles, (ii) the condensation and evaporation of n-alkanes, and (iii) dry deposition. The chemical transformation of gas-phase compounds was not taken into account. It was not necessary to model the nucleation of gas-phase vapors, as the computations were started with roadside conditions. Dry deposition and coagulation of particles were identified to be the most important aerosol dynamic processes that control the evolution and removal of particles. The effect of condensation and evaporation of organic vapors emitted by vehicles on particle numbers and on particle size distributions was examined. Under inefficient dispersion conditions, condensational growth contributed significantly to the evolution of PN from roadside to the neighborhood scale. The simplified parameterization of aerosol processes can predict particle number concentrations between roadside and the urban background with an inaccuracy of ∼ 10 %, compared to the fully size-resolved MAFOR model.

scholarly journals The effects of neighbourhood and workplace income comparisons on subjective wellbeing

2021 ◽  
Author(s):  
◽  
Shakked Noy
Keyword(s):  
Income Distribution ◽  
Subjective Wellbeing ◽  
Causal Effect ◽  
Peer Groups ◽  
Sensitivity Analyses ◽  
Group Level ◽  
Mass Layoffs ◽  
Fairness Concerns ◽  
Linear Regressions ◽  
Over Time

<p>We investigate how the incomes of a person’s neighbours and coworkers affect her happiness, using survey data on subjective wellbeing linked to unprecedentedly rich administrative data on the characteristics of survey respondents’ peer groups. Linear regressions of subjective wellbeing on peer income variables establish that people care exclusively about their ordinal rank within their peer income distribution, that workplace rank matters much more than neighbourhood rank, and that workplace comparisons are driven primarily by fairness concerns. We confirm that our results reflect a causal effect of peer income by implementing sensitivity analyses, identifying off changes in peer income over time for immobile people, exploiting plausibly exogenous moves between workplaces triggered by mass layoffs, and testing for the effects of unobservable group-level confounders.</p>

scholarly journals A new purification technique to obtain specific size distribution of giant lipid vesicles using dual filtration

PLoS ONE ◽  
2021 ◽  
Vol 16 (7) ◽  
pp. e0254930
Author(s):  
Mohammad Abu Sayem Karal ◽  
Tawfika Nasrin ◽  
Marzuk Ahmed ◽  
Md. Kabir Ahamed ◽  
Shareef Ahammed ◽  
...  
Keyword(s):  
Size Distribution ◽  
Fluorescent Probe ◽  
Lognormal Distribution ◽  
Lipid Vesicles ◽  
Water Soluble ◽  
Size Distributions ◽  
Narrow Size Distribution ◽  
Purification Technique ◽  
Polycarbonate Membranes ◽  
Filtration Technique

A new purification technique is developed for obtaining distribution of giant unilamellar vesicles (GUVs) within a specific range of sizes using dual filtration. The GUVs were prepared using well known natural swelling method. For filtration, different combinations of polycarbonate membranes were implemented in filter holders. In our experiment, the combinations of membranes were selected with corresponding pore sizes–(i) 12 and 10 μm, (ii) 12 and 8 μm, and (iii) 10 and 8 μm. By these filtration arrangements, obtained GUVs size distribution were in the ranges of 6−26 μm, 5–38 μm and 5–30 μm, respectively. In comparison, the size distribution range was much higher for single filtration technique, for example, 6−59 μm GUVs found for a membrane with 12 μm pores. Using this technique, the water-soluble fluorescent probe, calcein, can be removed from the suspension of GUVs successfully. The size distributions were analyzed with lognormal distribution. The skewness became smaller (narrow size distribution) when a dual filtration was used instead of single filtration. The mode of the size distribution obtained in dual filtration was also smaller to that of single filtration. By continuing this process of purification for a second time, the GUVs size distribution became even narrower. After using an extra filtration with dual filtration, two different size distributions of GUVs were obtained at a time. This experimental observation suggests that different size specific distributions of GUVs can be obtained easily, even if GUVs are prepared by different other methods.

Variations in aerosol size distributions and deposition fractions in human body based on long-term observations (2007 to 2018)

2020 ◽  
Author(s):  
ChanJung An ◽  
Sang-woo Kim ◽  
Wonsik Choi
Keyword(s):  
Human Body ◽  
Lognormal Distribution ◽  
Fine Particles ◽  
Aerosol Size Distribution ◽  
Background Concentration ◽  
Radiological Protection ◽  
Size Distributions ◽  
Human Respiratory Tract ◽  
Factors Affecting

&lt;p&gt;Fine particles can reach deeply into various tracts in the human body, causing adverse health effects. In addition, particulate matter affects earth energy balance directly, scattering solar radiation, and indirectly, forming clouds and changing cloud properties. In these respects, understanding the variations of aerosol concentrations in each mode of aerosol size distributions and the factors affecting those variations, is important.&lt;/p&gt;&lt;p&gt;In this study, we attempted to separate each mode from the aerosol size distributions obtained from long-term observations with scanning mobility particle sizer (SMPS) (December 2007 to October 2018) in Jeju Island (Gosan, national background concentration network, 33.17&amp;#730;N, 126.12&amp;#730;E).&lt;/p&gt;&lt;p&gt;The particle number size distributions (54 channels, from 10.4 nm to 469.8 nm) were separated into three modes using a fitting method based on the multiple lognormal distribution function. We then attempted to examine how these modes of particles have changed in time, and what factors (air trajectories, meteorology, other pollutants, and others) were related to the variations in each mode. We also calculated the deposition fractions of inhaled aerosols in each human respiratory tract from the observed size distributions using the International Commission on Radiological Protection (ICRP) deposition model, and we examined how these deposition fractions vary in different air quality conditions.&lt;/p&gt;&lt;p&gt;More details in the discussion concerning temporal variations in aerosol size distributions, the factors affecting those variations, and variations in deposition fractions in the human body are presented.&lt;/p&gt;&lt;p&gt;Keywords: aerosol, size distribution, deposition fraction, lognormal distribution mode.&lt;/p&gt;&lt;p&gt;&amp;#160;&lt;/p&gt;

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