s05.pdf
... data. This creates an empirical distribution. A simple empirical distribution can be produced from given data by piecewise linear approximation. Assume the available data points (observations) are arranged in increasing order x1 ; x2 ; :::; xn . Assume also that a probability is assigned to each res ...
... data. This creates an empirical distribution. A simple empirical distribution can be produced from given data by piecewise linear approximation. Assume the available data points (observations) are arranged in increasing order x1 ; x2 ; :::; xn . Assume also that a probability is assigned to each res ...
LLN, CLT - UCLA Statistics
... The first two inequalities specify loose bounds on probabilities knowing only µ (Markov) or µ and (Chebyshev), when the distribution is not known. They are also used to prove other limit results, such as LLN. ...
... The first two inequalities specify loose bounds on probabilities knowing only µ (Markov) or µ and (Chebyshev), when the distribution is not known. They are also used to prove other limit results, such as LLN. ...
homeworke_ch3
... 2. The arithmetic mean is the sum of the observations divided by the total number of observations. 3. For a set of data arranged or sorted in numerical order, the value of the observation in the center is called the weighted mean. 4. A set of ordinal, interval or ratio level data may only have one m ...
... 2. The arithmetic mean is the sum of the observations divided by the total number of observations. 3. For a set of data arranged or sorted in numerical order, the value of the observation in the center is called the weighted mean. 4. A set of ordinal, interval or ratio level data may only have one m ...
Chapter 1
... b. The two samples are independent because the patients involved cannot be taking both the medicine and the placebo, thus they are independent. 5. A real estate agent claims that there is no difference between the mean household incomes from two neighborhoods. The mean income of 12 randomly selected ...
... b. The two samples are independent because the patients involved cannot be taking both the medicine and the placebo, thus they are independent. 5. A real estate agent claims that there is no difference between the mean household incomes from two neighborhoods. The mean income of 12 randomly selected ...
chap01
... Discrete random variables yield numerical response that arise from a counting process ...
... Discrete random variables yield numerical response that arise from a counting process ...
Numerical Summary Measures of Variability for Data
... Remark 1: The 1.5 x IQR Criterion for Outliers An observation is called an outlier if it is 1.5*IQR larger than Q3 or 1.5*IQR smaller than Q1. Extreme outlier may indicate data entry error or unusual characteristics in the data that need careful investigation (if it is 3*IQR larger than Q3 or 3*IQR ...
... Remark 1: The 1.5 x IQR Criterion for Outliers An observation is called an outlier if it is 1.5*IQR larger than Q3 or 1.5*IQR smaller than Q1. Extreme outlier may indicate data entry error or unusual characteristics in the data that need careful investigation (if it is 3*IQR larger than Q3 or 3*IQR ...
document
... Sample size less than 15: Use t procedures if the data appear close to Normal (symmetric, single peak, no outliers). If the data are skewed or if outliers are present, do not use t. Sample size at least 15: The t procedures can be used except in the presence of outliers or strong skew-ness in th ...
... Sample size less than 15: Use t procedures if the data appear close to Normal (symmetric, single peak, no outliers). If the data are skewed or if outliers are present, do not use t. Sample size at least 15: The t procedures can be used except in the presence of outliers or strong skew-ness in th ...
Bootstrapping (statistics)
In statistics, bootstrapping can refer to any test or metric that relies on random sampling with replacement. Bootstrapping allows assigning measures of accuracy (defined in terms of bias, variance, confidence intervals, prediction error or some other such measure) to sample estimates. This technique allows estimation of the sampling distribution of almost any statistic using random sampling methods. Generally, it falls in the broader class of resampling methods.Bootstrapping is the practice of estimating properties of an estimator (such as its variance) by measuring those properties when sampling from an approximating distribution. One standard choice for an approximating distribution is the empirical distribution function of the observed data. In the case where a set of observations can be assumed to be from an independent and identically distributed population, this can be implemented by constructing a number of resamples with replacement, of the observed dataset (and of equal size to the observed dataset).It may also be used for constructing hypothesis tests. It is often used as an alternative to statistical inference based on the assumption of a parametric model when that assumption is in doubt, or where parametric inference is impossible or requires complicated formulas for the calculation of standard errors.