scholarly journals Biases in galaxy cluster velocity dispersion and mass estimates in the small Ngal regime

2020 ◽  
Vol 641 ◽  
pp. A41 ◽  
Author(s):  
A. Ferragamo ◽  
J. A. Rubiño-Martín ◽  
J. Betancort-Rijo ◽  
E. Munari ◽  
B. Sartoris ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Velocity Dispersion ◽  
Galaxy Cluster ◽  
Mean Velocity ◽  
Massive Galaxies ◽  
Unbiased Estimators ◽  
Dispersion Estimate ◽  
Physical Effects ◽  
The Mean ◽  
Selection Of

Aims. We present a study of the statistical properties of three velocity dispersion and mass estimators: biweight, gapper, and standard deviation for a small number of galaxies (Ngal ≤ 75). Methods. Using a set of 73 numerically simulated galaxy clusters, we first characterised the statistical bias and the variance for each one of the three estimators (biweight, gapper, and standard deviation) in the determination of the velocity dispersion and the dynamical mass of the clusters through the σ–M relation. These results were used to define a new set of unbiased estimators that are able to correct for these statistical biases with a minimum increase in associated variance. We also used the same set of numerical simulations to characterise two other physical biases that affect the estimates: the effect of velocity segregation on the selection of cluster members, and the effect of using cluster members within different physical radii from the cluster centre. Results. The standard deviation (and its unbiased counterpart) is the estimator with the lowest variance estimator after the biweight and gapper. The effect of velocity segregation in the selection of galaxies within the sub-sample of the most massive galaxies in the cluster introduces a bias of 2% in the velocity dispersion estimate when it is calculated using a quarter of the most massive cluster members. We also find a dependence of the velocity dispersion estimate on the aperture radius as a fraction of R200. This is consistent with previous results in the literature. Conclusions. The proposed set of unbiased estimators effectively provides a correction of the velocity dispersion and mass estimates from the statistical and physical effects discussed above for small numbers of cluster members. When these new estimators are applied to a subset of simulated observations, they can retrieve bias-corrected values for the mean velocity dispersion and the mean mass; the standard deviation has the lowest variance. Although for a single galaxy cluster the statistical and physical effects discussed here are comparable to or slightly smaller than the bias introduced by interlopers, they are relevant when ensemble properties and scaling relations for large number of clusters are studied.

scholarly journals Biases in the estimation of velocity dispersions and dynamical masses for galaxy clusters

2020 ◽  
Vol 228 ◽  
pp. 00011
Author(s):  
A. Ferragamo ◽  
J.A. Rubiño-Martín ◽  
J. Betancort-Rijo ◽  
E. Munari ◽  
B. Sartoris ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Galaxy Clusters ◽  
Velocity Dispersion ◽  
Mean Velocity ◽  
Dynamical Mass ◽  
Unbiased Estimators ◽  
The Mean ◽  
Velocity Dispersions ◽  
Dynamical Masses

Using a set of 73 numerically simulated galaxy clusters, we have characterised the statistical and physical biases for three velocity dispersion and mass estimators, namely biweight, gapper and standard deviation, in the small number of galaxies regime (Ngal ≤ 75), both for the determination of the velocity dispersion and the dynamical mass of the clusters via the σ–M relation. These results are used to define a new set of unbiased estimators, that are able to correct for those statistical biases. By applying these new estimators to a subset of simulated observations, we show that they can retrieve bias-corrected values for both the mean velocity dispersion and the mean mass.

SPECIAL ARTICLE

PEDIATRICS ◽  
1954 ◽  
Vol 14 (5) ◽  
pp. 563-564
Author(s):  
Keyword(s):  
Standard Deviation ◽  
Visual Assessment ◽  
Probable Error ◽  
Oral Examination ◽  
Frequency Curve ◽  
Written Examination ◽  
Lower Figure ◽  
Normal Frequency ◽  
The Mean ◽  
Selection Of

THE WRITTEN examination of January 15, 1954, was taken by 515 candidates, a larger number than in any previous year except 1953 when there were 607 candidates Grades ranged from a lowest mark of 32.0 to a highest mark of 89.5 Inspection of the range resulted in the decision to place the passing mark at 51. On this basis there were 32, or 6.2%, who failed and were therefore ineligible for oral examination. The distribution of the grades earned by the 515 candidates is presented in the form of a histogram. As an aid to visual assessment of the nature of the distribution, a normal frequency curve computed from the mean and standard deviation of the data has been superimposed on the diagram. The distribution of the grades is clearly and impressively skewed to the left, that is, the scores tend to be massed at the high end of the scale and spread out at the low end. An examination of this type is relatively sensitive in the zone of poorer scholarship where the selection of failures is to be made and relatively insensitive in the range of higher scholarship. The intrinsic reliability of the examination has again been assessed by comparing the grade made by each candidate on his odd-numbered questions with that earned on his even-numbered questions. The comparison reveals a "probable error of estimate," P.E.m, of 2.39, a lower figure and therefore a higher degree of reliability than yielded by any previous examination. The Committee is pleased that the increase in reliability was accomplished in spite of the fact that the length of the examination was decreased from 250 grading points in 1953 to 200 grading points.

scholarly journals On the Origin of the Standardization Sensitivity in RegEM Climate Field Reconstructions*

2008 ◽  
Vol 21 (24) ◽  
pp. 6710-6723 ◽  
Author(s):  
Jason E. Smerdon ◽  
Alexey Kaplan ◽  
Diana Chang
Keyword(s):  
Standard Deviation ◽  
Missing Values ◽  
Mean Field ◽  
Alternative Methods ◽  
Reconstruction Method ◽  
Climate Data ◽  
The Mean ◽  
Calibration Interval ◽  
Reconstruction Interval ◽  
Selection Of

Abstract The regularized expectation maximization (RegEM) method has been used in recent studies to derive climate field reconstructions of Northern Hemisphere temperatures during the last millennium. Original pseudoproxy experiments that tested RegEM [with ridge regression regularization (RegEM-Ridge)] standardized the input data in a way that improved the performance of the reconstruction method, but included data from the reconstruction interval for estimates of the mean and standard deviation of the climate field—information that is not available in real-world reconstruction problems. When standardizations are confined to the calibration interval only, pseudoproxy reconstructions performed with RegEM-Ridge suffer from warm biases and variance losses. Only cursory explanations of this so-called standardization sensitivity of RegEM-Ridge have been published, but they have suggested that the selection of the regularization (ridge) parameter by means of minimizing the generalized cross validation (GCV) function is the source of the effect. The origin of the standardization sensitivity is more thoroughly investigated herein and is shown not to be associated with the selection of the ridge parameter; sets of derived reconstructions reveal that GCV-selected ridge parameters are minimally different for reconstructions standardized either over both the reconstruction and calibration interval or over the calibration interval only. While GCV may select ridge parameters that are different from those that precisely minimize the error in pseudoproxy reconstructions, RegEM reconstructions performed with truly optimized ridge parameters are not significantly different from those that use GCV-selected ridge parameters. The true source of the standardization sensitivity is attributable to the inclusion or exclusion of additional information provided by the reconstruction interval, namely, the mean and standard deviation fields computed for the complete modeled dataset. These fields are significantly different from those for the calibration period alone because of the violation of a standard EM assumption that missing values are missing at random in typical paleoreconstruction problems; climate data are predominantly missing in the preinstrumental period when the mean climate was significantly colder than the mean of the instrumental period. The origin of the standardization sensitivity therefore is not associated specifically with RegEM-Ridge, and more recent attempts to regularize the EM algorithm using truncated total least squares could theoretically also be susceptible to the problems affecting RegEM-Ridge. Nevertheless, the principal failure of RegEM-Ridge arises because of a poor initial estimate of the mean field, and therefore leaves open the possibility that alternative methods may perform better.

scholarly journals Revisiting the functional response in habitat selection for large herbivores: a matter of spatial variation in resource distribution?

2019 ◽  
Vol 30 (6) ◽  
pp. 1725-1733 ◽  
Author(s):  
Antoine Duparc ◽  
Mathieu Garel ◽  
Pascal Marchand ◽  
Dominique Dubray ◽  
Daniel Maillard ◽  
...  
Keyword(s):  
Standard Deviation ◽  
Habitat Selection ◽  
Spatial Variation ◽  
Functional Response ◽  
Resource Distribution ◽  
Habitat Characteristics ◽  
High Rate ◽  
Large Herbivores ◽  
The Mean ◽  
Selection Of

Abstract Most habitats are distributed heterogeneously in space, forcing animals to move according to both habitat characteristics and their needs for energy and safety. Animal space use should therefore vary according to habitat characteristics, a process known as the “functional response” in habitat selection. This response has often been tested vis-à-vis the proportion of a habitat category within areas available to individuals. Measuring sought-after resources in landscape where they are continuously distributed is a challenge and we posit here that both the mean availability of a resource and its spatial variation should be measured. Accordingly, we tested for a functional response in habitat selection according to these two descriptors of the resource available for a mountain herbivore. We hypothesized that selection should decrease with mean value of resources available and increase with its spatial variation. Based on GPS data from 50 chamois females and data on the actual foodscape (i.e., distribution of edible-only biomass in the landscape), we estimated individual selection ratio (during summer months) for biomass at the home range level, comparing edible biomass in individual home ranges and the mean and standard deviation of edible biomass in their available range. Chamois being a group-living species, available accessible ranges were shared by several individuals that formed socio-spatial groups (clusters) in the population. As expected, selection ratios increased with the standard deviation of edible resources in each cluster, but unlike our prediction, was unrelated to its mean. Selection of areas richer in resources hence did not fade away when more resources were available on average, a result that may be explained by the need for this capital breeder species to accumulate fat-reserve at a high rate during summer months. Low spatial variation could limit the selection of chamois, which highlights the importance of resource distribution in the process of habitat selection.

A Comparison of Techniques for Particle Rebound Measurement in Gas Turbine Applications

2015 ◽  
Author(s):  
Jeffrey P. Bons ◽  
Rory Blunt ◽  
Steven Whitaker
Keyword(s):  
Standard Deviation ◽  
Velocity Distribution ◽  
Gas Turbine ◽  
Correlation Coefficient ◽  
Strong Dependence ◽  
Individual Particle ◽  
Aluminum Surface ◽  
Trajectory Data ◽  
Mean Velocity ◽  
The Mean

The rebound characteristics of 100–500μm quartz particles from an aluminum surface were imaged using the particle shadow velocimetry (PSV) technique. Particle trajectory data were acquired over a range of impact velocity (30–90 m/s) and impact angle (20°–90°) typical for gas turbine applications. The data were then analyzed to obtain coefficients of restitution (CoR) using four different techniques: (1) individual particle rebound velocity divided by the same particle’s inbound velocity (2) individual particle rebound velocity divided by inbound velocity taken from the mean of the inbound distribution of velocities from all particles (3) rebound velocity distribution divided by inbound velocity distribution related using distribution statistics and (4) the same process as (3) with additional precision provided by the correlation coefficient between the two distributions. It was found that the mean and standard deviation of the CoR prediction showed strong dependence on the standard deviation of the inbound velocity distribution. The two methods that employed statistical algorithms to account for the distribution shape [methods (3) and (4)] actually overpredicted mean CoR by up to 6% and CoR standard deviation by up to 100% relative to method (1). The error between the methods is shown to be a strong (and linear) function of correlation coefficient, which is typically 0.2–0.6 for experimental CoR data. Non-Gaussianity of the distributions only accounts for up to 1% of the error in mean CoR, and this largely from the non-zero skewness of the inbound velocity distribution. Particle rebound data acquired using field average techniques that do not provide an estimate of correlation coefficient are most accurately evaluated using method (2). Method (3) can be used with confidence if the standard deviation of the inbound velocity distribution is less than 10% of the mean velocity, or if a linear correction based on an assumed correlation coefficient is applied.

scholarly journals Correlation between Personality Types and Color Shade Preference

2014 ◽  
Vol 1 (4) ◽  
Author(s):  
Divya Ghorawat ◽  
Ravina Madan
Keyword(s):  
Standard Deviation ◽  
Preference Test ◽  
Personality Types ◽  
Personality Test ◽  
Age Group ◽  
Colour Preference ◽  
Individual Personality ◽  
The Mean ◽  
The Difference ◽  
Selection Of

The main aim of this study was to find out whether the color shade preferences of individuals, grouped according to their personality types are alike or not. The researchers also tried to study the difference in color shade preferences based on gender differences. The objective was to understand whether the color shade preferences of individuals are affected by their individual personality types or not and whether gender plays any role in selection of color shades of individuals. The study sample consisted of a total of 80 subjects, randomly selected from within the age group of 18-25. An attempt was made to maintain a balance between two genders and across the ages. The research instruments used were Eysenck’s Personality Test (to measure the personality types) and a separate Colour Bar- Colour Preference Test was designed to serve the purpose of this study. The subjects were made to fill both the questionnaires and then the items were scored and results were analyzed. Positive scoring was done for Eysenck’s personality questionnaire and negative scoring was used to score the Colour Bar-Colour Preference Test. The data collected was divided into: Introverts (female, male) and Extroverts (female, male). From the data collected the mean, standard deviation and correlation between extraversion scores and the most preferred colour scores, for all the four groups. The mean, standard deviation, and correlation for the four groups was found to be 436.4 (IF), 529.2 (IM), 504 (EF), 453.4 (EM); 5.47 (IF), 6.52 (IM), 5.48 (EF), 6.93(EM); -0.3 (IF), -0.1 (IM), 0.1 (EF) and 0.5 (EM) respectively. From this the conclusion was drawn that there was no significant correlation found between the personality types and colour shade preferences of the subjects except in the case of extroverted males. Recommendations: Increase the sample size as that proved to be a limitation to this study. A study across ages is also possible and might give different results.

scholarly journals CURRENTS IN THE SURF ZONE

2000 ◽  
Vol 1 (2) ◽  
pp. 3 ◽  
Author(s):  
D. L. Inman ◽  
W. H. Quinn
Keyword(s):  
Standard Deviation ◽  
Friction Coefficient ◽  
Velocity Distribution ◽  
Surf Zone ◽  
Longshore Current ◽  
Mean Velocity ◽  
Single Observation ◽  
Bottom Currents ◽  
Longshore Currents ◽  
The Mean

Surface and bottom currents in the surf zone were measured at 15 equally spaced points along two straight beaches with approximately parallel bottom contours. The measurements showed that offshore currents predominate over onshore currents at the bottom, while at the surface there is a slight predominance in the onshore direction. With regard to the longshore component, it was found that surface and bottom currents have a similar velocity distribution. The variability of the longshore component as measured by its standard deviation is equal to or larger than the mean longshore velocity. This wide variation in longshore currents indicates the impracticability of estimating the mean velocity from a single observation of longshore current. It was found that the momentum approach to the prediction of longshore currents by Putnam, Munk and Traylor (1949) leads to useful forecasts provided the beach friction coefficient k is permitted to vary with the longshore velocity, V. The indicated relation is k~v^(-3/2).

scholarly journals Velocity dispersions and metallicities of box-shaped galaxies

1993 ◽  
Vol 153 ◽  
pp. 411-412
Author(s):  
R. E. de Souza ◽  
S. dos Anjos ◽  
B. Barbuy
Keyword(s):  
Velocity Dispersion ◽  
Mean Velocity ◽  
The Mean ◽  
Velocity Dispersions ◽  
Disk Component

Velocity dispersions and Mg2 indices were measured from CCD spectra of 13 S0 box-shaped galaxies and 5 ellipticals. Evidence for a different relation between velocity dispersion and metallicity, relative to ellipticals, was found for our S0 sample; we attribute this difference to the S0 disk component, affecting both the mean velocity dispersion and mean metallicity.

367. Bacterial growth in reconstituted spray-dried milk

1948 ◽  
Vol 15 (3) ◽  
pp. 285-291 ◽  
Author(s):  
Constance Higginbottom
Keyword(s):  
Standard Deviation ◽  
Bacterial Growth ◽  
Food Poisoning ◽  
Spore Count ◽  
Fresh Milk ◽  
Standard Deviation Range ◽  
The Mean ◽  
Reconstituted Milk ◽  
Spray Dried ◽  
Selection Of

1. Over 200 samples of spray-dried milks from eight British plants have been examined for total and spore counts, numbers of β-haemolytic colonies and for moulds, yeasts and conliform bacteria.2. The mean count and standard deviation range for total and spore count are reported. No β-haemolytic colonies other than those due to spore-forming bacilli were detected.3. After ageing the reconstituted milk for 24 hr. at 15–5° C. the mean count (37° C.) was unchanged; at 22° C. the increase was 2000-fold and at 37° C. the milk had clotted within this time.4. The predominating organisms in a random selection of the reconstituted milks are described, both for the fresh milk and after ageing at 15·5 and 22° C. A marked increase i n spore-forming bacilli was noted at 22° C.5. The relation of the flora of reconstituted milk to its food-poisoning potentialities is briefly discussed.

Deep spectroscopy in nearby galaxy clusters – V. The Perseus cluster

2020 ◽  
Vol 494 (2) ◽  
pp. 1681-1692
Author(s):  
J A L Aguerri ◽  
M Girardi ◽  
I Agulli ◽  
A Negri ◽  
C Dalla Vecchia ◽  
...  
Keyword(s):  
Velocity Dispersion ◽  
Galaxy Cluster ◽  
Correlation Technique ◽  
Nearby Galaxy ◽  
Mean Velocity ◽  
Cluster Membership ◽  
Cluster Galaxies ◽  
Gap Technique ◽  
Red Galaxies ◽  
Perseus Cluster

ABSTRACT Dwarfs are the largest population of galaxies in number in the nearby Universe. Deep spectroscopic data are still missing to obtain a better understanding of their formation and evolution processes. This study shows the results obtained from a spectroscopic campaign in the Perseus cluster. We have obtained 963 new galaxy spectra. We have measured the recessional velocity of the galaxies by using a cross-correlation technique. These data have been used to obtain the cluster membership, the dynamics of the galaxies, and the spectroscopic luminosity function (LF) of the cluster. The cluster membership was obtained by using the peak + gap technique, reporting a total of 403 galaxies as cluster members within 1.4r200. The mean velocity and velocity dispersion of the cluster galaxies are Vc = 5258 km s−1 and σc = 1040 km s−1, respectively. We obtained M200 = 1.2 × 1015 M⊙ and r200 = 2.2 Mpc for this cluster. The clusters members were classified blue and red according to their g − r stellar colour. The velocity dispersion of these two families of galaxies is different, indicating that the blue galaxies can be classified as recently accreted into the cluster. We present the spectroscopic galaxy LF of the cluster. This function turned to be flat: α = 0.99 ± 0.06. In addition, blue and red galaxies show similar densities in the faint end of the LF. This indicates that Perseus does not have a population of red dwarf galaxias as large as other nearby clusters. We have compared the LF of the Perseus cluster with other spectroscopic LFs of nearby clusters and those from cosmological simulations. This comparison shows that the spectroscopic LF of nearby galaxy cluster is far from universal.

Sign in / Sign up

Export Citation Format

Share Document