scholarly journals Peak fitting and integration uncertainties for the Aerodyne Aerosol Mass Spectrometer

2015 ◽  
Vol 8 (4) ◽  
pp. 3471-3523 ◽  
Author(s):  
J. C. Corbin ◽  
A. Othman ◽  
J. D. Haskins ◽  
J. D. Allan ◽  
B. Sierau ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Model ◽  
Routine Data ◽  
Real Data ◽  
Peak Height ◽  
Data Set ◽  
Mass Spectrometers ◽  
Aerosol Mass ◽  
Peak Fitting ◽  
Uncertainty Model

Abstract. The errors inherent in the fitting and integration of the pseudo-Gaussian ion peaks in Aerodyne High-Resolution Aerosol Mass Spectrometers (HR-AMS's) have not been previously addressed as a source of imprecision for these instruments. This manuscript evaluates the significance of these uncertainties and proposes a method for their estimation in routine data analysis. Peak-fitting uncertainties, the most complex source of integration uncertainties, are found to be dominated by errors in m/z calibration. These calibration errors comprise significant amounts of both imprecision and bias, and vary in magnitude from ion to ion. The magnitude of these m/z calibration errors is estimated for an exemplary data set, and used to construct a Monte Carlo model which reproduced well the observed trends in fits to the real data. The empirically-constrained model is used to show that the imprecision in the fitted height of isolated peaks scales linearly with the peak height (i.e., as n1), thus contributing a constant-relative-imprecision term to the overall uncertainty. This constant relative imprecision term dominates the Poisson counting imprecision term (which scales as n0.5) at high signals. The previous HR-AMS uncertainty model therefore underestimates the overall fitting imprecision. The constant relative imprecision in fitted peak height for isolated peaks in the exemplary data set was estimated as ~4% and the overall peak-integration imprecision was approximately 5%. We illustrate the importance of this constant relative imprecision term by performing Positive Matrix Factorization (PMF) on a~synthetic HR-AMS data set with and without its inclusion. Finally, the ability of an empirically-constrained Monte Carlo approach to estimate the fitting imprecision for an arbitrary number of known overlapping peaks is demonstrated. Software is available upon request to estimate these error terms in new data sets.

scholarly journals Peak-fitting and integration imprecision in the Aerodyne aerosol mass spectrometer: effects of mass accuracy on location-constrained fits

2015 ◽  
Vol 8 (11) ◽  
pp. 4615-4636 ◽  
Author(s):  
J. C. Corbin ◽  
A. Othman ◽  
J. D. Allan ◽  
D. R. Worsnop ◽  
J. D. Haskins ◽  
...  
Keyword(s):  
Monte Carlo ◽  
Empirical Analysis ◽  
Quantitative Estimation ◽  
Peak Height ◽  
Data Set ◽  
Monte Carlo Approach ◽  
Peak Integration ◽  
Aerosol Mass ◽  
Peak Fitting ◽  
Overlapping Peaks

Abstract. The errors inherent in the fitting and integration of the pseudo-Gaussian ion peaks in Aerodyne high-resolution aerosol mass spectrometers (HR-AMSs) have not been previously addressed as a source of imprecision for these or similar instruments. This manuscript evaluates the significance of this imprecision and proposes a method for their estimation in routine data analysis. In the first part of this work, it is shown that peak-integration errors are expected to scale linearly with peak height for the constrained-peak-shape fits performed in the HR-AMS. An empirical analysis is undertaken to investigate the most complex source of peak-integration imprecision: the imprecision in fitted peak height, σh. It is shown that the major contributors to σh are the imprecision and bias inherent in the m/z calibration, both of which may arise due to statistical and physical non-idealities of the instrument. A quantitative estimation of these m/z-calibration imprecisions and biases show that they may vary from ion to ion, even for ions of similar m/z. In the second part of this work, the empirical analysis is used to constrain a Monte Carlo approach for the estimation of σh and thus the peak-integration imprecision. The estimated σh for selected well-separated peaks (for which m/z-calibration imprecision and bias could be quantitatively estimated) scaled linearly with peak height as expected (i.e. as n1). In combination with the imprecision in peak-width quantification (which may be easily and directly estimated during quantification), peak-fitting imprecisions therefore dominate counting imprecisions (which scale as n0.5) at high signals. The previous HR-AMS uncertainty model therefore underestimates the overall fitting imprecision even for well-resolved peaks. We illustrate the importance of this conclusion by performing positive matrix factorization on a synthetic HR-AMS data set both with and without its inclusion. In the third part of this work, the Monte Carlo approach is extended to the case of an arbitrary number of overlapping peaks. Here, a modification to the empirically constrained approach was needed, because the ion-specific m/z-calibration bias and imprecision can generally only be estimated for well-resolved peaks. The modification is to simply overestimate the m/z-calibration imprecision in all cases. This overestimation results in only a slight overestimate of σh, while significantly reducing the sensitivity of σh to the unknown, ion-specific m/z-calibration biases. Thus, with only the measured data and an approximate estimate of the order of magnitude of m/z-calibration biases as input, conservative and unbiased estimates of peak-integration imprecisions may be obtained for each peak in any ensemble of overlapping peaks.

scholarly journals Inferences for Weibull parameters under progressively first-failure censored data with binomial random removals

2020 ◽  
Vol 9 (1) ◽  
pp. 47-60
Author(s):  
Samir K. Ashour ◽  
Ahmed A. El-Sheikh ◽  
Ahmed Elshahhat
Keyword(s):  
Monte Carlo ◽  
Censored Data ◽  
Real Data ◽  
Unknown Parameters ◽  
Data Set ◽  
Monte Carlo Simulation Study ◽  
Squared Error Loss Function ◽  
Bayes Estimates ◽  
Monte Carlo Techniques ◽  
Credible Intervals

In this paper, the Bayesian and non-Bayesian estimation of a two-parameter Weibull lifetime model in presence of progressive first-failure censored data with binomial random removals are considered. Based on the s-normal approximation to the asymptotic distribution of maximum likelihood estimators, two-sided approximate confidence intervals for the unknown parameters are constructed. Using gamma conjugate priors, several Bayes estimates and associated credible intervals are obtained relative to the squared error loss function. Proposed estimators cannot be expressed in closed forms and can be evaluated numerically by some suitable iterative procedure. A Bayesian approach is developed using Markov chain Monte Carlo techniques to generate samples from the posterior distributions and in turn computing the Bayes estimates and associated credible intervals. To analyze the performance of the proposed estimators, a Monte Carlo simulation study is conducted. Finally, a real data set is discussed for illustration purposes.

scholarly journals Inverted Topp-Leone Distribution: Contribution to a Family of J-Shaped Frequency Functions in Presence of Random Censoring

2021 ◽  
Author(s):  
Hiba Zeyada Muhammed ◽  
Essam Abd Elsalam Muhammed
Keyword(s):  
Monte Carlo ◽  
Real Data ◽  
Posterior Density ◽  
Data Set ◽  
Bayes Estimates ◽  
Squared Error ◽  
Distribution Shape ◽  
Highest Posterior Density Intervals ◽  
Metropolis Hasting Algorithm ◽  
Highest Posterior Density

In this paper, Bayesian and non-Bayesian estimation of the inverted Topp-Leone distribution shape parameter are studied when the sample is complete and random censored. The maximum likelihood estimator (MLE) and Bayes estimator of the unknown parameter are proposed. The Bayes estimates (BEs) have been computed based on the squared error loss (SEL) function and using Markov Chain Monte Carlo (MCMC) techniques. The asymptotic, bootstrap (p,t), and highest posterior density intervals are computed. The Metropolis Hasting algorithm is proposed for Bayes estimates. Monte Carlo simulation is performed to compare the performances of the proposed methods and one real data set has been analyzed for illustrative purposes.

scholarly journals Goodness of fit for stochastic actor-oriented models

2019 ◽  
Vol 12 (3) ◽  
pp. 205979911988428 ◽  
Author(s):  
Josh Lospinoso ◽  
Tom AB Snijders
Keyword(s):  
Monte Carlo ◽  
Mahalanobis Distance ◽  
Goodness Of Fit ◽  
Real Data ◽  
Testing Procedure ◽  
Network Evolution ◽  
Data Set ◽  
Modified Model ◽  
Fit Testing ◽  
Distance Estimator

We propose a Mahalanobis distance–based Monte Carlo goodness of fit testing procedure for the family of stochastic actor-oriented models for social network evolution. A modified model distance estimator is proposed to help the researcher identify model extensions that will remediate poor fit. A limited simulation study is provided to establish baseline legitimacy for the Mahalanobis distance–based Monte Carlo test and modified model distance estimator. A forward model selection workflow is proposed, and this procedure is demonstrated on a real data set.

scholarly journals A Study of Perks-II Distribution via Bayesian Paradigm

Pravaha ◽  
2018 ◽  
Vol 24 (1) ◽  
pp. 1-17
Author(s):  
A. K. Chaudhary
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Real Data ◽  
Simulation Method ◽  
Mcmc Methods ◽  
Data Set ◽  
Bayesian Paradigm ◽  
Mcmc Simulation

In this paper, the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of Perks-II distribution based on a complete sample. The procedures are developed to perform full Bayesian analysis of the Perks-II distributions using Markov Chain Monte Carlo (MCMC) simulation method in OpenBUGS, established software for Bayesian analysis using Markov Chain Monte Carlo (MCMC) methods. We have obtained the Bayes estimates of the parameters, hazard and reliability functions, and their probability intervals are also presented. We have also discussed the issue of model compatibility for the given data set. A real data set is considered for illustration under gamma sets of priors.PravahaVol. 24, No. 1, 2018,page: 1-17 

scholarly journals Estimation for Entropy and Parameters of Generalized Bilal Distribution under Adaptive Type II Progressive Hybrid Censoring Scheme

Entropy ◽  
2021 ◽  
Vol 23 (2) ◽  
pp. 206
Author(s):  
Xiaolin Shi ◽  
Yimin Shi ◽  
Kuang Zhou
Keyword(s):  
Monte Carlo ◽  
Likelihood Estimation ◽  
Real Data ◽  
Random Variable ◽  
Credible Interval ◽  
Mcmc Methods ◽  
Type Ii ◽  
Data Set ◽  
Lindley’S Approximation ◽  
Bayesian Estimations

Entropy measures the uncertainty associated with a random variable. It has important applications in cybernetics, probability theory, astrophysics, life sciences and other fields. Recently, many authors focused on the estimation of entropy with different life distributions. However, the estimation of entropy for the generalized Bilal (GB) distribution has not yet been involved. In this paper, we consider the estimation of the entropy and the parameters with GB distribution based on adaptive Type-II progressive hybrid censored data. Maximum likelihood estimation of the entropy and the parameters are obtained using the Newton–Raphson iteration method. Bayesian estimations under different loss functions are provided with the help of Lindley’s approximation. The approximate confidence interval and the Bayesian credible interval of the parameters and entropy are obtained by using the delta and Markov chain Monte Carlo (MCMC) methods, respectively. Monte Carlo simulation studies are carried out to observe the performances of the different point and interval estimations. Finally, a real data set has been analyzed for illustrative purposes.

scholarly journals A New Generalized Family of Odd Lindley-G Distributions With Application

2019 ◽  
Vol 8 (6) ◽  
pp. 1
Author(s):  
Fastel Chipepa ◽  
Broderick O. Oluyede ◽  
Boikanyo Makubate
Keyword(s):  
Monte Carlo ◽  
Maximum Likelihood ◽  
Hazard Rate ◽  
Real Data ◽  
Maximum Likelihood Estimates ◽  
Data Set ◽  
Lorenz Curves ◽  
New Family ◽  
Special Cases ◽  
Family Of Distributions

A new family of distributions, namely the Kumaraswamy Odd Lindley-G distribution is developed. The new density function can be expressed as a linear combination of exponentiated-G densities. Statistical properties of the new family including hazard rate and quantile functions, moments and incomplete moments, Bonferroni and Lorenz curves, distribution of order statistics and R´enyi entropy are derived. Some special cases are presented. We conduct some Monte Carlo simulations to examine the consistency of the maximum likelihood estimates. We provide an application of KOL-LLo distribution to a real data set.

scholarly journals A Bayesian Analysis of Perks Distribution via Markov Chain Monte Carlo Simulation

2013 ◽  
Vol 14 (1) ◽  
pp. 153-166 ◽  
Author(s):  
Arun Kumar Chaudhary ◽  
Vijay Kumar
Keyword(s):  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Bayesian Analysis ◽  
Real Data ◽  
Simulation Method ◽  
Complete Sample ◽  
Data Set ◽  
Mcmc Simulation ◽  
The Given

In this paper the Markov chain Monte Carlo (MCMC) method is used to estimate the parameters of Perks distribution based on a complete sample. The procedures are developed to perform full Bayesian analysis of the Perks distributions using MCMC simulation method in OpenBUGS. We obtained the Bayes estimates of the parameters, hazard and reliability functions, and their probability intervals are also presented. We also discussed the issue of model compatibility for the given data set. A real data set is considered for illustration under gamma sets of priors. Nepal Journal of Science and Technology Vol. 14, No. 1 (2013) 153-166 DOI: http://dx.doi.org/10.3126/njst.v14i1.8936

PARAMETER ESTIMATE WITH ONLY ONE COMPLETE FAILURE OBSERVATION USING MONTE CARLO EM ALGORITHM

2001 ◽  
Vol 08 (02) ◽  
pp. 109-122 ◽  
Author(s):  
WAN-KAI PANG ◽  
PING-KEI LEUNG ◽  
XIAO-LONG PU ◽  
SHI-SONG MAO
Keyword(s):  
Monte Carlo ◽  
Weibull Distribution ◽  
Real Data ◽  
Model Parameters ◽  
Reliability Model ◽  
Estimation Of Parameters ◽  
Data Set ◽  
Failure Data ◽  
Mcem Algorithm ◽  
Monte Carlo Em

In reliability studies, often we only have one failure data recorded in a life testing experiment. If there are two parameters in the reliability model, such as the model using Weibull distribution, then maximum likelihood estimation of parameters becomes a difficult problem. Mao and Chen published a real data set of the lifetime of a certain type of bearings which only contains one failure data. They used a Bayesian method to analyze the data and obtained some results for model parameter estimation. However, in their method the choice of prior distribution will affect heavily the final results. In this paper, we propose a Monte Carlo EM (MCEM) algorithm to estimate reliability model parameters using the Weibull distribution. Based on the same data set of Mao and Chen, we obtain some results using the MCEM algorithm. Our results do not depend on the choice of arbitrary prior distributions.

scholarly journals Estimation Methods of Alpha Power Exponential Distribution with Applications to Engineering and Medical Data

2020 ◽  
pp. 149-166 ◽  
Author(s):  
Mazen Nassar ◽  
Ahmed Z. Afify ◽  
Mohammed Shakhatreh
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Simulations ◽  
Exponential Distribution ◽  
Real Data ◽  
Medical Data ◽  
Estimation Methods ◽  
Alpha Power ◽  
Unknown Parameters ◽  
Data Set ◽  
Distribution Parameters

This paper addresses the estimation of the unknown parameters of the alphapower exponential distribution (Mahdavi and Kundu, 2017) using nine frequentist estimation methods. We discuss the nite sample properties of the parameterestimates of the alpha power exponential distribution via Monte Carlo simulations. The potentiality of the distribution is analyzed by means of two real datasets from the elds of engineering and medicine. Finally, we use the maximumlikelihood method to derive the estimates of the distribution parameters undercompeting risks data and analyze one real data set.

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