Cumulative Distribution Estimation via Control Theoretic Smoothing Splines

2010 ◽  
pp. 95-104 ◽  
Author(s):  
Janelle K. Charles ◽  
Shan Sun ◽  
Clyde F. Martin
Keyword(s):  
Smoothing Splines ◽  
Cumulative Distribution ◽  
Distribution Estimation

scholarly journals Monotone Smoothing Splines with Bounds

2020 ◽  
Vol 169 (1) ◽  
pp. 613-627
Author(s):  
Sara Maad Sasane
Keyword(s):  
Existence And Uniqueness ◽  
Optimization Problem ◽  
Smoothing Splines ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Uniqueness Of Solutions ◽  
Spline Curve ◽  
Cumulative Distribution Functions ◽  
Finite Dimensional ◽  
Constrained Minimization Problem

Abstract The problem of monotone smoothing splines with bounds is formulated as a constrained minimization problem of the calculus of variations. Existence and uniqueness of solutions of this problem is proved, as well as the equivalence of it to a finite dimensional but nonlinear optimization problem. A new algorithm for computing the solution which is a spline curve, using a branch and bound technique, is presented. The method is applied to examples in neuroscience and for fitting cumulative distribution functions from data.

Probability distribution estimation for Web service QoS based on max entropy principle

2013 ◽  
Vol 32 (10) ◽  
pp. 2728-2731
Author(s):  
Zhi-hua DAI ◽  
Xiao-dong FU ◽  
Yuan HUANG ◽  
Nan JIA
Keyword(s):  
Probability Distribution ◽  
Web Service ◽  
Distribution Estimation ◽  
Entropy Principle

Evaluation for estimating of the PDF and the CDF of Generalized Inverted Exponential Distribution with Application in Industry

2020 ◽  
pp. 507-522
Author(s):  
Parisa Torkaman
Keyword(s):  
Least Squares ◽  
Exponential Distribution ◽  
Mean Squared Error ◽  
Weighted Least Squares ◽  
Real Data ◽  
Minimum Variance ◽  
Cumulative Distribution ◽  
Estimation Methods ◽  
Data Set ◽  
Better Than

The generalized inverted exponential distribution is introduced as a lifetime model with good statistical properties. This paper, the estimation of the probability density function and the cumulative distribution function of with five different estimation methods: uniformly minimum variance unbiased(UMVU), maximum likelihood(ML), least squares(LS), weighted least squares (WLS) and percentile(PC) estimators are considered. The performance of these estimation procedures, based on the mean squared error (MSE) by numerical simulations are compared. Simulation studies express that the UMVU estimator performs better than others and when the sample size is large enough the ML and UMVU estimators are almost equivalent and efficient than LS, WLS and PC. Finally, the result using a real data set are analyzed.

Feminisation of Multidimensional Poverty in Rural Odisha

2020 ◽  
Author(s):  
Surya Narayan Biswal ◽  
◽  
S. K. Mishra ◽  
M. K. Sarangi ◽  
◽  
...  
Keyword(s):  
Rural Areas ◽  
Social Groups ◽  
Multidimensional Poverty ◽  
Cumulative Distribution ◽  
Policy Framework ◽  
Living Standard ◽  
Individual Level ◽  
Multidimensional Poverty Index ◽  
Order Stochastic Dominance ◽  
The Individual

UNDP’s 2030 agenda of Sustainable Development Goals (SDGs) emphasized gender equality in augmenting human capital and alleviating poverty. For eradication of extreme poverty and building resilience for persons who are vulnerable to poverty, SDGs calls for a pro-poor and gender-sensitive policy framework. In this context, a gender-based study on multi-dimensional aspects of poverty is highly significant. Extant literature reveals that females are more deprived in different dimensions of poverty such as education, health, living standard, empowerment, environment, autonomy and social relationship. The present study is conducted with the basic objective of examining feminization of poverty in rural areas of Jagatsinghapur district of Odisha. Seven socio-economic dimensions comprising sixteen indicators have been taken into consideration to construct the Multidimensional Poverty Index (MPI) using the Alkire-Foster (AF) Method at the individual level. The novelty of the study lies in analyzing MPI at the individual level for rural Odisha. Higher female deprivation is observed across social groups and all occupation categories except services. Dummy variable regression analysis also supports the major findings of the study. Complementary Cumulative Distribution Function satisfies strict first-order stochastic dominance condition and substantiates the feminisation of poverty at each level of poverty cut-off across all social groups and occupational categories except for services. The findings of the study have significant implications for developing suitable policies for gender equalization and poverty alleviation.

Bootstrap Analysis

2017 ◽  
Author(s):  
Russell Cheng
Keyword(s):  
Goodness Of Fit ◽  
Null Distribution ◽  
Real Data ◽  
Confidence Regions ◽  
Confidence Bands ◽  
Cumulative Distribution ◽  
Attractive Alternative ◽  
Bootstrap Analysis ◽  
Parametric Bootstrapping ◽  
Anderson Darling

Parametric bootstrapping (BS) provides an attractive alternative, both theoretically and numerically, to asymptotic theory for estimating sampling distributions. This chapter summarizes its use not only for calculating confidence intervals for estimated parameters and functions of parameters, but also to obtain log-likelihood-based confidence regions from which confidence bands for cumulative distribution and regression functions can be obtained. All such BS calculations are very easy to implement. Details are also given for calculating critical values of EDF statistics used in goodness-of-fit (GoF) tests, such as the Anderson-Darling A2 statistic whose null distribution is otherwise difficult to obtain, as it varies with different null hypotheses. A simple proof is given showing that the parametric BS is probabilistically exact for location-scale models. A formal regression lack-of-fit test employing parametric BS is given that can be used even when the regression data has no replications. Two real data examples are given.

POWER LAW AND STRETCHED EXPONENTIAL EFFECTS OF EXTREME EVENTS IN CHINESE STOCK MARKETS

2010 ◽  
Vol 09 (02) ◽  
pp. 203-217 ◽  
Author(s):  
XIAOJUN ZHAO ◽  
PENGJIAN SHANG ◽  
YULEI PANG
Keyword(s):  
Correlation Analysis ◽  
Power Law ◽  
Extreme Events ◽  
Stock Markets ◽  
Cross Correlation ◽  
Extreme Values ◽  
Cumulative Distribution ◽  
Stretched Exponential ◽  
Cross Correlation Analysis ◽  
Chinese Stock Markets

This paper reports the statistics of extreme values and positions of extreme events in Chinese stock markets. An extreme event is defined as the event exceeding a certain threshold of normalized logarithmic return. Extreme values follow a piecewise function or a power law distribution determined by the threshold due to a crossover. Extreme positions are studied by return intervals of extreme events, and it is found that return intervals yield a stretched exponential function. According to correlation analysis, extreme values and return intervals are weakly correlated and the correlation decreases with increasing threshold. No long-term cross-correlation exists by using the detrended cross-correlation analysis (DCCA) method. We successfully introduce a modification specific to the correlation and derive the joint cumulative distribution of extreme values and return intervals at 95% confidence level.

scholarly journals Variability in Estimated Modelled Insulin Secretion

2021 ◽  
pp. 193229682199112
Author(s):  
Jennifer J. Ormsbee ◽  
Hannah J. Burden ◽  
Jennifer L. Knopp ◽  
J. Geoffrey Chase ◽  
Rinki Murphy ◽  
...  
Keyword(s):  
Insulin Secretion ◽  
Kinetic Parameters ◽  
Pancreatic Beta Cells ◽  
Compartment Model ◽  
Interquartile Range ◽  
Cumulative Distribution ◽  
Model Framework ◽  
Intravenous Glucose ◽  
C Peptide ◽  
Model Based

Background: The ability to measure insulin secretion from pancreatic beta cells and monitor glucose-insulin physiology is vital to current health needs. C-peptide has been used successfully as a surrogate for plasma insulin concentration. Quantifying the expected variability of modelled insulin secretion will improve confidence in model estimates. Methods: Forty-three healthy adult males of Māori or Pacific peoples ancestry living in New Zealand participated in an frequently sampled, intravenous glucose tolerance test (FS-IVGTT) with an average age of 29 years and a BMI of 33 kg/m2. A 2-compartment model framework and standardized kinetic parameters were used to estimate endogenous pancreatic insulin secretion from plasma C-peptide measurements. Monte Carlo analysis (N = 10 000) was then used to independently vary parameters within ±2 standard deviations of the mean of each variable and the 5th and 95th percentiles determined the bounds of the expected range of insulin secretion. Cumulative distribution functions (CDFs) were calculated for each subject for area under the curve (AUC) total, AUC Phase 1, and AUC Phase 2. Normalizing each AUC by the participant’s median value over all N = 10 000 iterations quantifies the expected model-based variability in AUC. Results: Larger variation is found in subjects with a BMI > 30 kg/m2, where the interquartile range is 34.3% compared to subjects with a BMI ≤ 30 kg/m2 where the interquartile range is 24.7%. Conclusions: Use of C-peptide measurements using a 2-compartment model and standardized kinetic parameters, one can expect ~±15% variation in modelled insulin secretion estimates. The variation should be considered when applying this insulin secretion estimation method to clinical diagnostic thresholds and interpretation of model-based analyses such as insulin sensitivity.

scholarly journals Do galactic bars depend on environment?: an information theoretic analysis of Galaxy Zoo 2

2020 ◽  
Vol 501 (1) ◽  
pp. 994-1001
Author(s):  
Suman Sarkar ◽  
Biswajit Pandey ◽  
Snehasish Bhattacharjee
Keyword(s):  
Spatial Distribution ◽  
Mutual Information ◽  
Local Density ◽  
Statistical Significance ◽  
Distribution Functions ◽  
Cumulative Distribution ◽  
Host Galaxy ◽  
Data Sets ◽  
Data Set ◽  
Information Theoretic

ABSTRACT We use an information theoretic framework to analyse data from the Galaxy Zoo 2 project and study if there are any statistically significant correlations between the presence of bars in spiral galaxies and their environment. We measure the mutual information between the barredness of galaxies and their environments in a volume limited sample (Mr ≤ −21) and compare it with the same in data sets where (i) the bar/unbar classifications are randomized and (ii) the spatial distribution of galaxies are shuffled on different length scales. We assess the statistical significance of the differences in the mutual information using a t-test and find that both randomization of morphological classifications and shuffling of spatial distribution do not alter the mutual information in a statistically significant way. The non-zero mutual information between the barredness and environment arises due to the finite and discrete nature of the data set that can be entirely explained by mock Poisson distributions. We also separately compare the cumulative distribution functions of the barred and unbarred galaxies as a function of their local density. Using a Kolmogorov–Smirnov test, we find that the null hypothesis cannot be rejected even at $75{{\ \rm per\ cent}}$ confidence level. Our analysis indicates that environments do not play a significant role in the formation of a bar, which is largely determined by the internal processes of the host galaxy.

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