(Tiểu luận) midterm reportsampling distribution estimation

Sampling distribution In the case of the vendor rating study, the researchers assumed that the performance scores for each vendor were normally distributed.. In this study, interval esti

NATIONAL ECONOMICS UNIVERSITY

ADVANCED EDUCATION PROGRAM

-*** -MIDTERM REPORT

SAMPLING DISTRIBUTION & ESTIMATION Instructor: Assoc Prof., Tran Thi Bich

Subject: Business Statistics

Class: Advanced Finance 63D

Group: 1

Group Members: Đinh Xuân Anh (Leader) – 11210327

Vũ Lê Minh – 11213981 Trần Thu Phương – 11216961

Lê Kim Ngân – 11214201 Nguyễn Tấn Dũng - 11211502 Hoàng Bảo Ngọc Diệp – 11211304

I Table of Contents

I Table of Contents 1

II Part 1: Main Article 2

Purpose of the study 2

Dataset 2

Methodology 2

Analysis 3

a The meaning of the results 3

b Reason why the method was recommended to be used 3

c Additional Sampling distribution and Estimation possible for this article 4

III Part 2: Additional Article 5

Article 1: Estimation of incubation period distribution of COVID-19 using disease onset forward time: A novel cross-sectional and forward follow-up study 5

a Sampling distribution 5

b Estimation 7

Article #2: Posttraumatic Stress Disorder and Functioning and Quality of Life Outcomes in a Nationally Representative Sample of Male Vietnam Veterans (1997) 8

a Sampling distribution 8

b Esstimation 8

IV Part 3: Application 9

1 General information 9

2 Sampling method + sampling distribution 10

2 Estimation 11

3 Implication 13

V REFERENCES 14

II Part 1: Main Article

Artical analysis “Vendor rating in purchasing scenario: a confidence interval appoarch”

https://sci-hub.ru/https://doi.org/10.1108/01443570110404736

Purpose of the study

The selected article provides information about the process of evaluation and assessment of suppliers based on various criteria to make informed decisions regarding the selection and management of suppliers in a supply chain The aim of vendor rating is to identify and rate vendors based on their performance, capabilities, and suitability for the organization's procurement needs

The specific issue of interest in the research paper titled "Vendor Rating in Purchasing Scenario: A Confidence Interval Approach" is to propose a methodology that addresses the drawbacks associated with the vendor rating process One of the challenges mentioned is the presence of bias in the estimation process To overcome this issue, the paper suggests utilizing a confidence interval approach for estimating the rating This approach involves considering the opinions and inputs of a group of decision-makers rather than relying solely on the judgment of a single decision-maker

By incorporating a confidence interval approach, the proposed methodology aims to provide

a more robust and reliable vendor rating process that reduces the impact of individual biases and provides a more accurate assessment of vendors This approach allows for a comprehensive evaluation of suppliers and helps in making well-informed decisions regarding supplier selection and management within the purchasing scenario

Dataset

 Various individuals have been drawn from different functions within an organization such

as materials, production, maintenance, purchasing, quality control and a few representatives from the shop floor

 The members have been selected based on their experience, knowledge of the company, etc

 The functional heterogeneity in such multifunctional teams is potentially an asset because new knowledge from the overall range of departments is brought into the process in its early phases, much of the cost and quality of the final product is determined

Methodology

a Sampling method and sampling distribution: stratified random sampling

method is recommended for selecting vendors for rating

b Estimation method: The estimation method used in the study was a confidence

interval estimation approach

In the formula for calculating the upper and lower confidence limit, the following assumptions are made:

 The data (rating) is from the normal distribution, and individuals are drawn from different functions, such as materials, purchasing, production, quality control department, etc This procedure of selecting the individuals from various functions is similar to stratified random sampling It involves a process of stratification of segregation of the organization into different functions, followed by a random selection of executives from each function with larger groups the central limit theorem is invoked to use the normal distribution

 The individual values of the composite rating are independent of each other

 Sample size (number of individuals) is adequate to use statistical confidence limits Analysis

a The meaning of the results

The results showed that the confidence interval approach provides a more comprehensive and accurate assessment of vendor performance The authors found that using statistical methods such

as confidence intervals can provide a measure of the precision and reliability of vendor ratings, which is useful for decision-making in the purchasing process The confidence intervals also provide a range of values within which the true rating is likely to lie, which helps in making informed decisions about supplier selection They found that the confidence interval approach is less subjective and provides a more accurate and reliable assessment of vendor performance

b Reason why the method was recommended to be used

Sampling method

Stratified random sampling is used because it ensures that the sample of vendors selected for rating is representative of the population of vendors from which they were drawn This can improve the accuracy of the vendor ratings by reducing the variability of the estimates and increasing the precision of the results

Sampling distribution

In the case of the vendor rating study, the researchers assumed that the performance scores for each vendor were normally distributed This assumption allowed them to use the properties of the normal distribution to calculate the mean and standard deviation of the performance scores, which are necessary for calculating confidence intervals

The use of a normal sampling distribution was appropriate in this case because the performance scores were continuous variables and were assumed to be normally distributed However, it is important to note that the assumption of normality should be tested and validated using statistical methods such as normal probability plots or tests for normality If the data does not follow a normal distribution, alternative sampling distributions and methods may need to be used

In this study, interval estimation was used to estimate the performance of each vendor and the level of confidence associated with these estimates Interval estimation involves using a range of values, called a confidence interval, to estimate an unknown parameter with a certain level of

confidence In this study, the researchers used a confidence interval approach to estimate the vendor's performance score with a 95% level of confidence

Specifically, they calculated a 95% confidence interval for each vendor's performance score, which provided a range of values that was likely to include the true performance score with a 95% level of confidence The width of the confidence interval reflects the amount of uncertainty associated with the estimate, with wider intervals indicating more uncertainty The use of point and interval estimation in this study allowed the researchers to estimate the vendor's performance with a certain level of confidence and to quantify the amount of uncertainty associated with these estimates

c Additional Sampling distribution and Estimation possible for this article

Sampling distribution

Beta Distribution: The beta distribution is a continuous probability distribution that is commonly used in quality control and reliability engineering The beta distribution could be used

to model the probability distribution of the performance score for each vendor This would allow for the calculation of confidence intervals for each vendor's performance score, which is the approach proposed by Muralidharan and Anantharaman

Estimation:

 Bayesian estimation: This method involves using prior knowledge or beliefs about the population parameter to make estimates In the vendor rating study, the researchers could have used Bayesian estimation to incorporate prior knowledge or beliefs about the performance of the vendors For example, if they had worked with the vendors before and had some idea of their performance, they could have used that information to adjust their estimates

 Maximum likelihood estimation: This method involves finding the value of the population parameter that maximizes the likelihood of observing the sample data In the vendor rating study, the researchers could have used maximum likelihood estimation to estimate the parameters of a statistical model, such as a linear regression model or a logistic regression model, that relates the vendor's performance to other variables, such as the size

of the purchase order or the complexity of the product

 Nonparametric estimation: This method involves estimating the population parameter using nonparametric methods that do not rely on assumptions about the underlying distribution of the data In the vendor rating study, the researchers could have used nonparametric estimation to estimate the performance of the vendors based on their rankings or ratings, without assuming a specific distribution

III Part 2: Additional Article

Article 1: Estimation of incubation period distribution of COVID-19 using disease onset forward time: A novel cross-sectional and forward follow-up study

a Sampling distribution

Weibull

Meaning

The Weibull distribution is used in the research to estimate the parameters of the incubation period distribution and describe its shape The estimated shape parameter is close to 1, suggesting

an approximately exponential distribution However, the Weibull distribution allows for deviations from exponential behavior, providing a flexible model Overall, the use of the Weibull distribution provides a widely used and flexible model for estimating the distribution parameters and shape of the COVID-19 incubation period

How they use it

The Weibull distribution is a probability model with shape (k) and scale (λ) parameters It's commonly used to model time until an event occurs The study applies the Weibull distribution to COVID-19 incubation period data, estimating k and λ from the data to model the distribution

Lognormal & Gamma

Meaning

 Lognormal

The authors compare the Weibull model to a lognormal distribution and find that it also fits well The lognormal distribution is used as an alternative model to estimate the incubation period distribution, showing good performance and viability as an alternative to the Weibull distribution

Discover more

from:

TKKD

Document continues below

Thống kê trong

kinh tế và kinh…

Đại học Kinh tế…

999+ documents

Go to course

Ôn thi- trắc nghiệm thống kế trong kinh…

Thống kê

trong… 100% (60)

51

Thống Kê Anh Huy

Thống kê

trong kin… 98% (66)

36

Bai Tập Môn Nguyen

Lý Thống Ke Bản đầ…

Thống kê

trong kin… 100% (11)

38

Giải BVN Buổi 1 Chương 1 đến 5

Thống kê

trong kin… 95% (22)

21

Vở-thống-kê ghi chép bài giảng và…

22

 Gamma

The gamma distribution is used in this research as the primary model to estimate the incubation period distribution of COVID-19 The authors show that the gamma distribution provides a good fit to the data and performs better than other commonly used distributions for this type of analysis

Thống kê trong kin… 100% (10)

He thong cong thuc mon nguyen ly thon…

Thống kê trong kin… 100% (8)

19

Estimates based on Gamma and lognormal distributions provide similar results, with slightly smaller log likelihoods than the Weibull distribution The average time from leaving Wuhan to symptom onset is 5.30 days, with a median of 5 days and a maximum of 22 days The fitted density function calculated in this research fits the observed forward times well, indicating the model's reasonability and trustworthy results Figure 2 shows the fitted density function in a solid line overlaid on the observed forward times histogram, with the Weibull probability density function for incubation period distribution shown in a dashed line

b Estimation

In the cohort of COVID-19 cases, they assume that the incubation period is a Weibull random variable; the estimates in the Weibull model can be obtained by maximizing the corresponding likelihood function

Definition of maximum likelihood: maximum likelihood works by finding the set of

parameter values that maximize the probability of observing the data This is done by constructing a likelihood function, which is a function that measures how well the model fits the data for a given set of parameter values The maximum likelihood estimate of the parameters is then the set of values that maximize the likelihood function

Estimate α and λ by maximizing the product of likelihoods, , with respect to α and

λ, where is the observed forward time of the th individual and is the sample size of thevi i I

studying cohort

Article #2: Posttraumatic Stress Disorder and Functioning and Quality of Life Outcomes in a Nationally Representative Sample of Male Vietnam Veterans (1997)

a Sampling distribution

The study population was stratified by geographical region, and then within each region, veterans were sampled based on their branch of service and military rank Furthermore, the study also used stratified sampling to assess the prevalence of PTSD among the veterans This approach ensured that the prevalence of PTSD was accurately estimated and representative of the larger population of male Vietnam veterans

In general, if the stratified sampling method was appropriately implemented, then the sampling distribution of the estimator should follow a normal distribution according to the Central Limit Theorem, if the sample sizes within each stratum are sufficiently large (typically, n

≥ 30) and the strata are approximately normally distributed

b Esstimation

Weighted point estimation:

Weighted point estimation is a statistical method that takes into account the complex survey design, including stratification and sampling weights, to produce nationally representative estimates

In the study, the weighted prevalence estimates were calculated for PTSD and other outcomes, such as depression, substance abuse, and quality of life measures These estimates were based on data collected from a representative sample of male Vietnam veterans, with oversampling of certain subgroups, such as minorities and those with high combat exposure Weighted point estimation allowed the researchers to produce accurate prevalence estimates for the study population and to draw meaningful conclusions about the relationship between PTSD and functioning and quality of life outcomes

Logistic regression:

Logistic regression is a statistical method used to model the probability of a binary outcome (such as the presence or absence of a disorder) as a function of one or more predictor variables (such as other psychiatric disorders) They use logistic regression models to estimate the adjusted odds ratios and 95% confidence intervals for the association between PTSD and each of the six functional outcomes These models adjust for potential confounding variables, including demographic characteristics and comorbid disorders