scholarly journals A Classroom Approach to Illustrate Transformation and Bootstrap Confidence Interval Techniques Using the Poisson Distribution

2017 ◽  
Vol 6 (2) ◽  
pp. 42 ◽  
Author(s):  
Per Gösta Andersson
Keyword(s):  
Problem Solving ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Poisson Distribution ◽  
Learning Process ◽  
Bootstrap Confidence Interval ◽  
New Techniques ◽  
Teacher Student ◽  
Bootstrap Techniques ◽  
Interval Estimator

The Poisson distribution is here used to illustrate transformation and bootstrap techniques in order to construct a confidence interval for a mean. A comparison is made between the derived intervals and the Wald  and score confidence intervals. The discussion takes place in a classroom, where the teacher and the students have previously discussed and evaluated the Wald and score confidence intervals. While step by step  interactively getting acquainted  with new techniques,  the students will learn about the effects of e.g. bias and asymmetry and ways of dealing with such phenomena. The primary purpose of this teacher-student communication is therefore not to find the  best possible interval estimator for this particular case, but rather to provide a study displaying a teacher and her/his students interacting with each other in an efficient and rewarding way. The teacher has a strategy of encouraging the students to take initiatives. This is accomplished by providing the necessary background of the problem and some underlying theory after which the students are confronted with questions and problem solving. From this the learning process starts. The teacher has to be flexible according to how the students react.  The students are supposed to have studied mathematical statistics for at least two semesters. 

BOOTSTRAP CONFIDENCE INTERVALS FOR STEADY-STATE AVAILABILITY

2004 ◽  
Vol 21 (03) ◽  
pp. 407-419 ◽  
Author(s):  
JAE-HAK LIM ◽  
SANG WOOK SHIN ◽  
DAE KYUNG KIM ◽  
DONG HO PARK
Keyword(s):  
Steady State ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Coverage Probability ◽  
Average Length ◽  
Repairable System ◽  
Bootstrap Confidence Interval ◽  
Bootstrap Confidence Intervals ◽  
Bootstrap Methods ◽  
Percentile Bootstrap

Steady-state availability, denoted by A, has been widely used as a measure to evaluate the reliability of a repairable system. In this paper, we develop new confidence intervals for steady-state availability based on four bootstrap methods; standard bootstrap confidence interval, percentile bootstrap confidence interval, bootstrap-t confidence interval, and bias-corrected and accelerated confidence interval. We also investigate the accuracy of these bootstrap confidence intervals by calculating the coverage probability and the average length of intervals.

scholarly journals ON THE NUMBER OF BOOTSTRAP REPETITIONS FOR BCa CONFIDENCE INTERVALS

2002 ◽  
Vol 18 (4) ◽  
pp. 962-984 ◽  
Author(s):  
Donald W.K. Andrews ◽  
Moshe Buchinsky
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
High Probability ◽  
Random Variables ◽  
American Statistical Association ◽  
Bootstrap Confidence Interval ◽  
Statistical Association ◽  
Step Method ◽  
Bootstrap Confidence Intervals ◽  
The Ideal

This paper considers the problem of choosing the number of bootstrap repetitions B to use with the BCa bootstrap confidence intervals introduced by Efron (1987, Journal of the American Statistical Association 82, 171–200). Because the simulated random variables are ancillary, we seek a choice of B that yields a confidence interval that is close to the ideal bootstrap confidence interval for which B = ∞. We specify a three-step method of choosing B that ensures that the lower and upper lengths of the confidence interval deviate from those of the ideal bootstrap confidence interval by at most a small percentage with high probability.

scholarly journals Assessing the Accuracy of Approximate Confidence Intervals Proposed for the Mean of Poisson Distribution

2020 ◽  
Vol 18 (1) ◽  
pp. 2-13
Author(s):  
Alireza Shirvani ◽  
Malek Fathizadeh
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Poisson Distribution ◽  
Count Data ◽  
Coverage Probability ◽  
Discrete Distribution ◽  
Interval Length ◽  
Average Confidence ◽  
The Mean ◽  
Approximate Confidence Intervals

The Poisson distribution is applied as an appropriate standard model to analyze count data. Because this distribution is known as a discrete distribution, representation of accurate confidence intervals for its distribution mean is extremely difficult. Approximate confidence intervals were presented for the Poisson distribution mean. The purpose of this study is to simultaneously compare several confidence intervals presented, according to the average coverage probability and accurate confidence coefficient and the average confidence interval length criteria.

scholarly journals The use of the bootstrap method for the assessment of investment effectiveness and risk – the case of confidence intervals estimation for the Sharpe ratio and TailVaR

2020 ◽  
Vol 1/2020 (13) ◽  
pp. 40-50
Author(s):  
Jarno Klaudia ◽  
◽  
Smaga Łukasz ◽  
Keyword(s):  
Confidence Interval ◽  
Confidence Intervals ◽  
Stock Exchange ◽  
Bootstrap Method ◽  
Interval Estimation ◽  
Sharpe Ratio ◽  
Estimation Methods ◽  
Bootstrap Confidence Interval ◽  
Warsaw Stock Exchange ◽  
Confidence Interval Estimation

This paper is aimed at presenting application of bootstrap interval estimation methods to the assessment of financial investment’s effectiveness and risk. At first, we give an overview of various methods of bootstrap confidence interval estimation, i.e. bootstrap-t interval, percentile interval and BCa interval. Then, bootstrap confidence interval estimation methods are used to estimate confidence intervals for the Sharpe ratio and TailVaR of the Warsaw Stock Exchange sectoral indices. The results show that the bootstrap confidence intervals of different types are quite similarly positioned for each of the analysed index and measure. Taking into the account the locations of confidence intervals for both the Sharpe ratio and TailVaR, the real estate sector tends to be the most advantageous from the investor’s viewpoint.

scholarly journals 13. Evolving Toward Laughter in Learning

2011 ◽  
Vol 1 ◽  
pp. 75
Author(s):  
William B. Strean
Keyword(s):  
Higher Education ◽  
Student Engagement ◽  
Problem Solving ◽  
Classroom Management ◽  
Learning Process ◽  
Learning Satisfaction ◽  
Teacher Student ◽  
Management Problems ◽  
Research Findings ◽  
The Relationship

Lowman (1995) described the relationship between teacher and student and student engagement as the two most important ingredients in learning in higher education. Humour builds teacher-student connection (Berk, 1998) and engages students in the learning process. The bond between student and teacher is essential for learning, satisfaction, and retention. Humour helps students to learn better, remember more, improve problem-solving, absorb and retain information more quickly, and reduce their anxiety about subjects like math and science. Humour also reduces classroom management problems. This essay reviews research findings that support the use of humour in teaching and it provides strategies that teachers can use to bring more humour into their classrooms.

Proses Berpikir Logis Siswa Sekolah Dasar Bertipe Kecerdasan Logis Matematis dalam Memecahkan Masalah Matematika

2014 ◽  
Vol 2 (2) ◽  
Author(s):  
Liska Yanti Pane ◽  
Kamid Kamid ◽  
Asrial Asrial
Keyword(s):  
Problem Solving ◽  
Learning Process ◽  
Qualitative Method ◽  
Logical Thinking ◽  
Think Aloud ◽  
Process Data ◽  
Thinking Process ◽  
Problem Solving Process ◽  
Problem Solving Strategy ◽  
Solving Strategy

This research aims to describe logical thinking process of a logical-mathematical intelligence student. We employ qualitative method to disclose the subject’s learning process. Data are collected by interview and modified think aloud methods. The results show that subject has capability to find and organize problems and data correctly. Subject describes conditions that are needed to do the steps of problem solving strategy. The steps are done systematically until the end of problem solving process.

Empirical Nonparametric Bootstrap Strategies in Quantitative Trait Loci Mapping: Conditioning on the Genetic Model

Genetics ◽  
1998 ◽  
Vol 148 (1) ◽  
pp. 525-535
Author(s):  
Claude M Lebreton ◽  
Peter M Visscher
Keyword(s):  
Quantitative Trait Loci ◽  
Confidence Interval ◽  
Confidence Intervals ◽  
Quantitative Trait ◽  
Genetic Factors ◽  
Genetic Model ◽  
Original Data ◽  
Nonparametric Bootstrap ◽  
Test Protocol ◽  
Trait Loci

AbstractSeveral nonparametric bootstrap methods are tested to obtain better confidence intervals for the quantitative trait loci (QTL) positions, i.e., with minimal width and unbiased coverage probability. Two selective resampling schemes are proposed as a means of conditioning the bootstrap on the number of genetic factors in our model inferred from the original data. The selection is based on criteria related to the estimated number of genetic factors, and only the retained bootstrapped samples will contribute a value to the empirically estimated distribution of the QTL position estimate. These schemes are compared with a nonselective scheme across a range of simple configurations of one QTL on a one-chromosome genome. In particular, the effect of the chromosome length and the relative position of the QTL are examined for a given experimental power, which determines the confidence interval size. With the test protocol used, it appears that the selective resampling schemes are either unbiased or least biased when the QTL is situated near the middle of the chromosome. When the QTL is closer to one end, the likelihood curve of its position along the chromosome becomes truncated, and the nonselective scheme then performs better inasmuch as the percentage of estimated confidence intervals that actually contain the real QTL's position is closer to expectation. The nonselective method, however, produces larger confidence intervals. Hence, we advocate use of the selective methods, regardless of the QTL position along the chromosome (to reduce confidence interval sizes), but we leave the problem open as to how the method should be altered to take into account the bias of the original estimate of the QTL's position.

More evidence on competing cognitive systems

1985 ◽  
Vol 1 (1) ◽  
pp. 47-72 ◽  
Author(s):  
Sascha W. Felix
Keyword(s):  
Second Language ◽  
Problem Solving ◽  
General Problem ◽  
Learning Process ◽  
Native Speaker ◽  
Universal Grammar ◽  
Learning Task ◽  
Competition Model ◽  
Cognitive Systems ◽  
Specific System

This paper deals with the question of why adults, as a rule, fail to achieve native-speaker competence in a second language, whereas children appear to be generally able to acquire full command of either a first or second language. The Competition Model proposed in this paper accounts for this difference in terms of different cognitive systems or modules operating in child and adult language acquisition. It is argued that the child's learning process is guided by a language-specific module, roughly equivalent to Universal Grammar (cf. Chomsky, 1980), while adults tend to approach the learning task by utilizing a general problem-solving module which enters into competition with the language-specific system. The crucial evidence in support of the Competition Model comes from a) the availability of formal operations in different modules and b) from differences in the types of utterances produced by children and adults.

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