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9781402016899

Advanced Sampling Theory With Applications

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  • ISBN13:

    9781402016899

  • ISBN10:

    1402016891

  • Format: Hardcover
  • Copyright: 2004-01-01
  • Publisher: Kluwer Academic Pub
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Summary

Advanced Sampling Theory with Applications: How Michael "selected" Amy is a comprehensive exposè of basic and advanced sampling techniques along with their applications in the diverse fields of science and technology. This book is a multi-purpose document. It can be used as a text by teachers, as a reference manual by researchers, and as a practical guide by statisticians. It covers 1165 references from different research journals through almost 1900 citations across 1194 pages, a large number of complete proofs of theorems, important results such as corollaries, and 324 unsolved exercises from several research papers. It includes 159 solved, data-based, real life numerical examples in disciplines such as Agriculture, Demography, Social Science, Applied Economics, Engineering, Medicine, and Survey Sampling. These solved examples are very useful for an understanding of the applications of advanced sampling theory in our daily life and in diverse fields of science. An additional 173 unsolved practical problems are given at the end of the chapters. University and college professors may find these useful when assigning exercises to students. Each exercise gives exposure to several complete research papers for researchers/students. The data-based problems show statisticians how to select a sample and obtain estimates of parameters from a given population by using different sampling strategies, systematic sampling, stratified sampling, cluster sampling, and multi-stage sampling. Derivations of calibration weights from the design weights under single phase and two-phase sampling have been provided for simple numerical examples. These examples will be useful to understand the meaning of benchmarks to improve the design weights. These examples also explain the background of well-known scientific computer packages like CALMAR, GES, SAS, STATA, and SUDAAN etc., used to generate calibration weights by most organizations in the public and private sectors. The ideas of hot deck, cold deck, mean method of imputation, ratio method of imputation, compromised imputation, and multiple imputations have been explained with very simple numerical examples. Simple examples are also provided to understand Jackknife variance estimation under single phase, two-phase [or random non-response by following Sitter (1997)] and multi-stage stratified designs. This book also covers, in a very simple and compact way, many new topics not yet available in any book on the international market. A few of these interesting topics are: median estimation under single phase and two-phase sampling, difference between low level and higher level calibration approach, calibration weights and design weights, estimation of parametric functions, hidden gangs in finite populations, compromised imputation, variance estimation using distinct units, general class of estimators of population mean and variance, wider class of estimators of population mean and variance, power transformation estimators, estimators based on the mean of non-sampled units of the auxiliary character, ratio and regression type estimators for estimating finite population variance similar to proposed by Isaki (1982), unbiased estimators of mean and variance under Midzuno's scheme of sampling, usual and modified jackknife variance estimator, estimation of regression coefficient, concept of revised selection probabilities, multi-character surveys sampling, overlapping, adaptive, and post cluster sampling, new techniques in systematic sampling, successive sampling, small area estimation, continuous populations, and estimation of measurement errors.

Table of Contents

Preface xxi
Basic Concepts and Mathematical Notation
Introduction
1(1)
Population
1(1)
Finite population
1(1)
Infinite population
1(1)
Target population
1(1)
Study population
1(1)
Sample
2(1)
Examples of populations and samples
2(1)
Census
2(1)
Relative aspects of sampling versus census
2(1)
Study variable
2(1)
Auxiliary variable
3(1)
Difference between study variable and auxiliary variable
3(1)
Parameter
3(1)
Statistic
3(1)
Statistics
4(1)
Sample selection
4(3)
Chit method or Lottery method
4(1)
With replacement sampling
4(1)
Without replacement sampling
5(1)
Random number table method
5(1)
Remainder method
6(1)
Probability sampling
7(1)
Probability of selecting a sample
7(1)
Population mean/total
8(1)
Population moments
8(1)
Population standard deviation
8(1)
Population coefficient of variation
8(1)
Relative mean square error
9(1)
Sample mean
9(1)
Sample variance
9(1)
Estimator
10(1)
Estimate
10(1)
Sample space
10(1)
Univariate random variable
11(1)
Qualitative random variables
11(1)
Quantitative random variables
11(1)
Discrete random variable
11(1)
Continuous random variable
11(1)
Probability mass function (p.m.f.) of a univariate discrete random variable
12(1)
Probability density function (p.d.f.) of a univariate continuous random variable
12(1)
Expected value and variance of a univariate random variable
13(1)
Distribution function of a univariate random variable
13(2)
Discrete distribution function
14(1)
Continuous distribution function
14(1)
Selection of a sample using known univariate distribution function
15(4)
Discrete random variable
15(2)
Continuous random variable
17(2)
Discrete bivariate random variable
19(1)
Joint probability distribution function of bivariate discrete random variables
20(1)
Joint cumulative distribution function of bivariate discrete random variables
20(1)
Marginal distributions of a bivariate discrete random variable
20(1)
Selection of a sample using known discrete bivariate distribution function
20(1)
Continuous bivariate random variable
21(1)
Joint probability distribution function of a bivariate continuous random variable
21(1)
Joint cumulative distribution function of a bivariate continuous random variable
22(1)
Marginal cumulative distributions of bivariate continuous random variable
22(1)
Selection of a sample using known bivariate continuous distribution function
22(2)
Properties of a best estimator
24(5)
Unbiasedness
24(4)
Bias
28(1)
Consistency
28(1)
Sufficiency
28(1)
Efficiency
29(1)
Variance
29(1)
Mean square error
29(1)
Relative efficiency
29(1)
Relative bias
29(1)
Variance estimation through splitting
30(1)
Loss function
31(1)
Admissible estimator
31(1)
Sample survey
31(1)
Sampling distribution
32(1)
Sampling frame
33(1)
Sample survey design
33(1)
Errors in the estimators
33(2)
Sampling errors
34(1)
Non-sampling errors
34(1)
Non-response errors
35(1)
Measurement errors
35(1)
Tabulation errors
35(1)
Computational errors
35(1)
Point estimator
35(1)
Interval estimator
35(1)
Confidence interval
35(3)
Population proportion
38(1)
Sample proportion
38(1)
Variance of sample proportion and confidence interval estimates
39(11)
Relative standard error
50(1)
Auxiliary information
50(6)
Some useful mathematical formulae
56(1)
Ordered statistics
57(2)
Population median
57(1)
Population quartiles
58(1)
Population percentiles
59(1)
Population mode
59(1)
Definition(s) of statistics
59(1)
Limitations of statistics
60(1)
Lack of confidence in statistics
60(1)
Scope of statistics
60(11)
Exercises
60(3)
Practical problems
63(8)
Simple Random Sampling
Introduction
71(1)
Simple random sampling with replacement
71(8)
Simple random sampling without replacement
79(15)
Estimation of population proportion
94(9)
Searls' estimator of population mean
103(3)
Use of distinct units in the WR sample at the estimation stage
106(12)
Estimation of mean
107(6)
Estimation of finite population variance
113(5)
Estimation of total or mean of a subgroup (domain) of a population
118(5)
Dealing with a rare attribute using inverse sampling
123(2)
Controlled sampling
125(2)
Determinant sampling
127(10)
Exercises
128(4)
Practical problems
132(5)
Use of Auxiliary Information: Simple Random Sampling
Introduction
137(1)
Notation and expected values
137(1)
Estimation of population mean
138(53)
Ratio estimator
138(7)
Product estimator
145(4)
Regression estimator
149(11)
Power transformation estimator
160(1)
A dual of ratio estimator
161(3)
General class of estimators
164(2)
Wider class of estimators
166(1)
Use of known variance of auxiliary variable at estimation stage of population mean
167(1)
A class of estimators
167(2)
A wider class of estimators
169(4)
Methods to remove bias from ratio and product type estimators
173(1)
Quenouille's method
173(2)
Interpenetrating sampling method
175(5)
Exactly unbiased ratio type estimator
180(3)
Unbiased product type estimator
183(2)
Class of almost unbiased estimators of population ratio and product
185(2)
Filtration of bias
187(4)
Estimation of finite population variance
191(12)
Ratio type estimator
192(5)
Difference type estimator
197(1)
Power transformation type estimator
198(1)
General class of estimators
199(4)
Estimation of regression coefficient
203(6)
Usual estimator
203(1)
Unbiased estimator
204(3)
Improved estimators of regression coefficient
207(2)
Estimation of finite population correlation coefficient
209(5)
Superpopulation model approach
214(9)
Relationship between linear model and regression estimator
214(3)
Improved estimator of variance of linear regression estimator
217(4)
Relationship between linear model and ratio estimator
221(2)
Jackknife variance estimator
223(6)
Ratio estimator
223(3)
Regression estimator
226(3)
Estimation of population mean using more than one auxiliary variable
229(16)
Multivariate ratio estimator
230(1)
Multivariate regression type estimators
231(8)
General class of estimators
239(6)
General class of estimators to estimate any population parameter
245(3)
Estimation of ratio or product of two population means
248(2)
Median estimation in survey sampling
250(45)
Exercises
257(24)
Practical problems
281(14)
Use of Auxiliary Information: Probability Proportional to Size and with Replacement (PPSWR) Sampling
Introduction
295(1)
What is PPSWR sampling?
295(11)
Cumulative total method
300(3)
Lahiri's method
303(3)
Estimation of population total
306(6)
Relative efficiency of PPSWR sampling with respect to SRSWR sampling
312(5)
Superpopulation model approach
312(3)
Cost aspect
315(2)
PPSWR sampling: More than one auxiliary variable is available
317(9)
Notation and expectations
318(1)
Class of estimators
319(1)
Wider class of estimators
320(4)
PPSWR sampling with negatively correlated variables
324(2)
Multi-character survey
326(13)
Study variables have poor positive correlation with the selection probabilities
326(9)
General class of estimators
335(1)
Study variables have poor positive as well as poor negative correlation with the selection probabilities
336(3)
Concept of revised selection probabilities
339(1)
Estimation of correlation coefficient using PPSWR sampling
340(9)
Exercises
341(4)
Practical problems
345(4)
Use of Auxiliary Information: Probability Proportional to Size and Without Replacement (PPSWOR) Sampling
Introduction
349(2)
Useful symbols
349(1)
Some mathematical relations
349(2)
Horvitz and Thompson estimator and related topics
351(22)
General class of estimators
373(2)
Model based estimation strategies
375(10)
A brief history of the superpopulation model
377(1)
Scott, Brewer and Ho's robust estimation strategy
378(5)
Design variance and anticipated variance of linear regression type estimator
383(2)
Construction and optimal choice of inclusion probabilities
385(14)
Pareto πps sampling estimation scheme
386(1)
Hanurav's method
387(1)
Brewer's method
388(1)
Sampford's method
389(1)
Narain's method
390(1)
Midzuno--Sen method
390(1)
Kumar--Gupta--Nigam scheme
391(1)
Dey and Srivastava scheme for even sample size
392(1)
SSS sampling scheme
393(1)
Optimal choice of first order inclusion probabilities
394(5)
Calibration approach
399(10)
Calibrated estimator of the variance of the estimator of population total
409(4)
Estimation of variance of Greg
413(6)
Improved estimator of variance of the GREG: The higher level calibration approach
419(9)
Recalibrated estimator of the variance of Greg
424(2)
Recalibration using optimal designs for the Greg
426(2)
Calibrated estimators of variance of estimator of total and distribution function
428(3)
Unified setup
430(1)
Calibration of estimator of variance of regression predictor
431(13)
Chaudhuri and Roy's results
433(3)
Calibrated estimators of variance of regression predictor
436(1)
Model assisted calibration
436(4)
Calibration estimators when variance of auxiliary variable is known
440(1)
Each component of Vx is known
441(1)
Compromized calibration
442(2)
Prediction variance
444(1)
Ordered and unordered estimators
444(8)
Ordered estimators
445(4)
Unordered estimators
449(3)
Rao--Hartley--Cochran (RHC) sampling strategy
452(10)
Unbiased strategies using IPPS sampling schemes
462(3)
Estimation of population mean using a ratio estimator
462(2)
Estimation of finite population variance
464(1)
Godambe's strategy: Estimation of parameters in survey sampling
465(14)
Optimal estimating function
470(2)
Regression type estimators
472(1)
Singh's strategy in two-dimensional space
473(3)
Godambe's strategy for linear Bayes and optimal estimation
476(3)
Unified theory of survey sampling
479(14)
Class of admissible estimators
479(1)
Estimator
479(1)
Admissible estimator
479(1)
Strictly admissible estimator
479(4)
Linear estimators of population total
483(2)
Admissible estimators of variances of estimators of total
485(1)
Condition for the unbiased estimator of variance
485(1)
Admissible and unbiased estimator of variance
485(1)
Fixed size sampling design
485(1)
Horvitz and Thompson estimator and its variance in two forms
485(4)
Polynomial type estimators
489(1)
Alternative optimality criterion
490(1)
Sufficient statistic in survey sampling
491(2)
Estimators based on conditional inclusion probabilities
493(1)
Current topics in survey sampling
494(3)
Survey design
495(1)
Data collection and processing
495(1)
Estimation and analysis of data
496(1)
Miscellaneous discussions/topics
497(7)
Generalized IPPS designs
497(1)
Tam's optimal strategies
498(1)
Use of ranks in sample selection
498(1)
Prediction approach
498(1)
Total of bottom (or top) percentiles of a finite population
499(1)
General form of estimator of variance
499(1)
Poisson sampling
499(1)
Cosmetic calibration
500(1)
Mixing of non-parametric models in survey sampling
501(3)
Golden Jubilee Year 2003 of the linear regression estimator
504(25)
Exercises
507(13)
Practical Problems
520(9)
Use of Auxiliary Information: Multi-Phase Sampling
Introduction
529(1)
SRSWOR scheme at the first as well as at the second phases of the sample selection
530(19)
Notation and expected values
530(2)
Ratio estimator
532(3)
Cost function
535(4)
Difference estimator
539(1)
Regression estimator
540(1)
General class of estimators of population mean
541(3)
Estimation of finite population variance
544(1)
Calibration approach in two-phase sampling
545(4)
Two-phase sampling using two auxiliary variables
549(5)
Chain ratio type estimators
554(1)
Calibration using two auxiliary variables
555(5)
Estimation of variance of calibrated estimator in two-phase sampling: low and higher level calibration
560(3)
Two-phase sampling using multi-auxiliary variables
563(1)
Unified approach in two-phase sampling
563(2)
Concept of three-phase sampling
565(2)
Estimation of variance of regression estimator under two-phase sampling
567(5)
Two-phase sampling using PPSWR sampling
572(4)
Concept of dual frame surveys
576(2)
Common variables used for further calibration of weights
576(1)
Estimation of variance using dual frame surveys
577(1)
Estimation of median using two-phase sampling
578(10)
General class of estimators
578(1)
Regression type estimator
579(2)
Position estimator
581(1)
Stratification estimator
582(2)
Optimum first and second phase samples for median estimation
584(1)
Cost is fixed
584(1)
Variance is fixed
584(1)
Kuk and Mak's technique in two-phase sampling
584(2)
Chen and Qin technique in two-phase sampling
586(2)
Distribution function with two-phase sampling
588(2)
Improved version of two-phase calibration approach
590(25)
Improved first phase calibration
590(2)
Improved second phase calibration
592(2)
Exercises
594(18)
Practical problems
612(3)
VOLUME II
Systematic Sampling
Introduction
615(1)
Systematic sampling
615(5)
Modified systematic sampling
620(1)
Circular systematic sampling
621(2)
PPS circular systematic sampling
623(1)
Estimation of variance under systematic sampling
624(3)
Sub-sampling or replicated sub-sampling scheme
625(1)
Successive differences
626(1)
Variance of circular systematic sampling
627(1)
Systematic sampling in population with linear trend
627(8)
Estimators with linear trend
627(2)
Modification of estimates
629(2)
Estimators based on centrally located samples
631(2)
Estimators based on balanced systematic sampling
633(2)
Singh and Singh's systematic sampling scheme
635(2)
Zinger strategy in systematic sampling
637(1)
Populations with cyclic or periodic trends
638(1)
Multi-dimensional systematic sampling
639(10)
Exercises
642(4)
Practical problems
646(3)
Stratified and Post-Stratified Sampling
Introduction
649(1)
Stratified sampling
650(9)
Different methods of sample allocation
659(17)
Equal allocation
659(1)
Proportional allocation
659(3)
Optimum allocation method
662(14)
Use of auxiliary information at estimation stage
676(20)
Separate ratio estimator
677(4)
Separate regression estimator
681(3)
Combined ratio estimator
684(4)
Combined regression estimator
688(5)
On degree of freedom in stratified random sampling
693(3)
Calibration approach for stratified sampling design
696(5)
Exact combined linear regression using calibration
700(1)
Construction of strata boundaries
701(11)
Strata boundaries for proportional allocation
702(1)
Strata boundaries for Neyman allocation
703(5)
Stratification using auxiliary information
708(4)
Superpopulation model approach
712(1)
Multi-way stratification
713(5)
Stratum boundaries for multi-variate populations
718(5)
Optimum allocation in multi-variate stratified sampling
723(3)
Stratification using two-phase sampling
726(3)
Post-stratified sampling
729(6)
Conditional post-stratification
730(1)
Unconditional post-stratification
731(4)
Estimation of proportion using stratified random sampling
735(30)
Exercises
738(10)
Practical problems
748(17)
Non-Overlapping, Overlapping, Post, and Adaptive Cluster Sampling
Introduction
765(1)
Non-overlapping clusters of equal size
766(24)
Optimum value of non-overlapping cluster size
790(2)
Estimation of proportion using non-overlapping cluster sampling
792(4)
Non-overlapping clusters of different sizes
796(9)
Selection of non-overlapping clusters with unequal probability sampling
805(3)
Optimal and robust strategies for non-overlapping cluster sampling
808(4)
Overlapping cluster sampling
812(5)
Population size is known
812(2)
Population size is unknown
814(3)
Post-cluster sampling
817(2)
Adaptive cluster sampling
819(10)
Exercises
820(2)
Practical problems
822(7)
Multi-Stage, Successive, and Re-Sampling Strategies
Introduction
829(1)
Notation
830(1)
Procedure for construction of estimators of the total
831(2)
Method of calculating the variance of the estimators
833(4)
Selection of first and second stage units using SRSWOR sampling
834(2)
Optimum allocation in two-stage sampling
836(1)
Optimum allocation of sample in three-stage sampling
837(1)
Modified three-stage sampling
838(1)
General class of estimators in two-stage sampling
839(3)
Prediction estimator under two-stage sampling
842(2)
Prediction approach to robust variance estimation in two-stage cluster sampling
844(3)
Royall's technique of variance estimation
846(1)
Two-stage sampling with successive occasions
847(18)
Arnab's successive sampling scheme
848(17)
Estimation strategies in supplemented panels
865(1)
Re-sampling methods
866(23)
Jackknife variance estimator
867(4)
Balanced half sample (BHS) method
871(2)
Bootstrap variance estimator
873(1)
Exercises
873(14)
Practical problems
887(2)
Randomized Response Sampling: Tools for Social Surveys
Introduction
889(1)
Pioneer model
889(3)
Franklin's model
892(5)
Unrelated question model and related issues
897(6)
When proportion of unrelated character is known
897(1)
When proportion of unrelated character is unknown
898(5)
Regression analysis
903(4)
Ridge regression estimator
905(2)
Hidden gangs in finite populations
907(9)
Two sample method
907(4)
One sample method
911(1)
Estimation of correlation coefficient between two characters of a hidden gang
912(4)
Unified approach for hidden gangs
916(4)
Randomized response technique for a quantitative variable
920(4)
Greg using scrambled responses
924(6)
Calibration of scrambled responses
925(3)
Higher order calibration of the estimators of variance under scrambled responses
928(2)
General class of estimators
930(1)
On respondent's protection: Qualitative characters
930(12)
Leysieffer and Warner's measure
930(2)
Lanke's measure
932(1)
Mangat and Singh's two-stage model
933(2)
Mangat and Singh's two-stage and Warner's model at equal level of protection
935(4)
Mangat's model
939(1)
Mangat's and Warner's model at equal level of protection
940(2)
On respondent's protection: Quantitative characters
942(7)
Unrelated question model for quantitative data
942(1)
The additive model
943(1)
The multiplicative model
943(1)
Measure of privacy protection
944(1)
Comparison between additive and multiplicative models
945(4)
Test for detecting untruthful answering
949(2)
Stochastic randomized response technique
951(24)
Exercises
954(18)
Practical problems
972(3)
Non-Response and its Treatments
Introduction
975(1)
Hansen and Hurwitz pioneer model
976(4)
Politz and Simmons model
980(4)
Horvitz and Thompson estimator under non-response
984(2)
Ratio and regression type estimators
986(14)
Distribution and some expected values
987(1)
Estimation of population mean
987(6)
Estimation of finite population variance
993(7)
Calibrated estimators of total and variance in the presence of non-response
1000(9)
Estimation of population total and variance
1000(2)
Calibration estimator for the total
1002(1)
Calibration of the estimators of variance
1003(2)
PPSWOR Sampling
1005(2)
SRSWOR Sampling
1007(2)
Different treatments of non-response
1009(4)
Ratio method of imputation
1010(1)
Mean method of imputation
1010(1)
Hot deck (HD) method of imputation
1010(1)
Nearest neighbor (NN) method of imputation
1011(2)
Superpopulation model approach
1013(3)
Different components of variance
1014(2)
Jackknife technique
1016(1)
Hot deck imputation for multi-stage designs
1017(4)
Multiple imputation
1021(4)
Degree of freedom with multiple imputation for small samples
1024(1)
Compromised imputation
1025(6)
Practicability of compromised imputation
1027(1)
Recommendations of compromised imputation
1027(1)
Warm deck imputation
1028(1)
Mean cum NN imputation
1028(3)
Estimation of response probabilities
1031(2)
Estimators based on estimated response probabilities
1033(32)
Estimators based on response probabilities
1035(2)
Calibration of response probabilities
1037(1)
Calibrated estimator and its variance
1038(1)
Estimation of variance of the calibrated estimator
1039(2)
Exercises
1041(17)
Practical problems
1058(7)
Miscellaneous Topics
Introduction
1065(1)
Estimation of measurement errors
1065(8)
Estimation of measurement error using a single measurement per element
1066(1)
Model and notation
1066(1)
Grubbs' estimators
1066(2)
Bhatia, Mangat, and Morrison's (BMM) repeated measurement estimators
1068(1)
Model and notation
1069(4)
Raking ratio using contingency tables
1073(4)
Continuous populations
1077(4)
Small area estimation
1081(24)
Symptomatic accounting techniques
1081(1)
Vital rates method (VRM)
1081(1)
Census component method (CCM)
1082(1)
Housing unit method (HUM)
1083(1)
Synthetic estimator
1083(3)
Composite estimator
1086(4)
Model based techniques
1090(1)
Henderson's model
1090(3)
Nested error regression model
1093(2)
Random regression coefficient model
1095(2)
Fay and Herriot model
1097(1)
Further generalizations
1097(2)
Estimation of proportion of a characteristic in small areas of a population
1099(2)
Exercises
1101(1)
Practical problems
1101(4)
Appendix
Tables
Pseudo-Random Numbers (PRN)
1105(2)
Critical values based on t distribution
1107(2)
Area under the standard normal curve
1109(2)
Populations
All operating banks: Amount (in $000) of agricultural loans outstanding in different states in 1997
1111(2)
Hypothetical situation of a small village having only 30 older persons (age more than 50 years): Approximate duration of sleep (in minutes) and age (in years) of the persons
1113(1)
Apples, commercial crop: Season average price (in $) per pound, by States, 1994---1996
1114(2)
Fish caught: Estimated number of fish caught by marine recreational fishermen by species group and year, Atlantic and Gulf coasts, 1992---1995
1116(3)
Tobacco: Area (hectares), yield and production (metric tons) in specified countries during 1998
1119(4)
Age specific death rates from 1990 to 2065 (Number per 100,000 births)
1123(1)
State population projections, 1995 and 2000 (Number in thousands)
1124(2)
Projected vital statistics by country or area during 2000
1126(3)
Number of immigrants admitted to the USA
1129(2)
Bibliography 1131(62)
Author Index 1193(22)
Handy Subject Index 1215(4)
Additional Information 1219

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

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