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The long-run cost curve is a cost function that models this minimum cost over time, meaning inputs are not fixed. Using the long-run cost curve, firms can scale their means of production to reduce the costs of producing the good. [1] There are three principal cost functions (or 'curves') used in microeconomic analysis:
The total cost curve, if non-linear, can represent increasing and diminishing marginal returns.. The short-run total cost (SRTC) and long-run total cost (LRTC) curves are increasing in the quantity of output produced because producing more output requires more labor usage in both the short and long runs, and because in the long run producing more output involves using more of the physical ...
The sample size is relatively small (say, n ≤ 10— ¯ and s charts are typically used for larger sample sizes) The sample size is constant; Humans must perform the calculations for the chart; As with the ¯ and s and individuals control charts, the ¯ chart is only valid if the within-sample variability is constant. [4]
The sample size is an important feature of any empirical study in which the goal is to make inferences about a population from a sample. In practice, the sample size used in a study is usually determined based on the cost, time, or convenience of collecting the data, and the need for it to offer sufficient statistical power .
The sample size is relatively large (say, n > 10— ¯ and R charts are typically used for smaller sample sizes) The sample size is variable; Computers can be used to ease the burden of calculation; The "chart" actually consists of a pair of charts: One to monitor the process standard deviation and another to monitor the process mean, as is ...
It says what fraction of the variance of the data is explained by the fitted trend line. It does not relate to the statistical significance of the trend line (see graph); the statistical significance of the trend is determined by its t-statistic. Often, filtering a series increases r 2 while making little difference to the fitted trend.
For a random variable X, the r th population L-moment is [1] = = () { : } , where X k:n denotes the k th order statistic (k th smallest value) in an independent sample of size n from the distribution of X and denotes expected value operator.
For finite values of , the efficiency is higher than this (for example, a sample size of 3 gives an efficiency of about 74%). [citation needed] The sample mean is thus more efficient than the sample median in this example. However, there may be measures by which the median performs better.
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