统计代写|R语言代写R language代考|SOW-BS086

统计代写|R语言代写R language代考|Other Distributions

You can use a variety of other distributions in a similar fashion; for full details look at the help entries by typing help (Distributions). Look at a few examples now to get a flavor of the possibilities. In the following example, you start the Poisson distribution by generating 50 random values:
The Poisson distribution has only a single parameter, lambda, equivalent to the mean. The next example uses the binomial distribution to assess probabilities:
$>\operatorname{pbinom}(c(3,6,9,12)$, size $=17$, prob $=0.5)$
[1] $0.0063630 .166153 \quad 0.685471 \quad 0.975479$
In this case you use pbinom () to calculate the cumulative probabilities in a binomial distribution. You have two additional parameters: size is the number of trials and prob is the probability of each trial being a success.
You can use the Student’s t-test to compare two normally distributed samples. In this following example you use the qt () command to determine critical values for the $t$-test for a range of degrees of freedom. You then go on to work out two-sided $p$-values for a range of $\mathrm{t}$-values:
$>\mathrm{qt}(0.975, \mathrm{df}=c(5,10,100$, Inf $))$
[1] $2.5712 .2281 .9841 .960$
$>(1-\operatorname{pt}(\mathrm{c}(1.6,1.9,2.2)$, df $=\operatorname{Inf})) * 2$
[1] $0.10960 \quad 0.05743 \quad 0.02781$
In the first case you set the cumulative probability to $0.975$; this will give you a 5 percent critical value, because effectively you want $2.5$ percent of each end of the distribution (because this is a symmetrical distribution you can take $2.5$ percent from each end to make your 5 percent). You put in several values for the degrees of freedom (related to the sample size). Notice that you can use Inf to represent infinity. The result shows you the value of $t$ you would have to get for the differences in your samples (their means) to be significantly different at the 5 percent level; in other words, you have determined the critical values.

In the second case you want to determine the two-sided $\mathrm{p}$-value for various values of $\mathrm{t}$ when the degrees of freedom are infinity. The pt () command would determine the cumulative probability if left to its own devices. So, you must subtract each one from 1 and then multiply by 2 (because you are taking a bit from each end of the distribution). You can get the same result using a modification of the command using the lower. tail = instruction. By default this is set to TRUE; this effectively means that you are reading the $\mathrm{x}$-axis from left to right. If you set the instruction to FALSE, you switch around and read the $\mathrm{x}$-axis from right to left. The upshot is that you do not need to subtract from one, which involves remembering where to place the brackets.

统计代写|R语言代写R language代考|The Kolmogorov-Smirnov Test

The Kolmogorov-Smirnov test enables you to compare two distributions. This means that you can either compare a sample to a “known” distribution or you can compare two unknown distributions to see if they are the same; effectively you are comparing the shape.

The command that allows you access to the Kolmogorov-Smirnov test is ks . test (), which fortunately is shorter than the actual name. You furnish the command with at least two instructions; the first being the vector of data you want to test and the second being the one you want to compare it to. This second instruction can be in various forms; you can provide a vector of numeric values or you can use a function, for example, pnorm (), in some way. In the following example you look to compare a sample to the normal distribution: In this case you specify the cumulative distribution function you want as a text string (that is, in quotes) and also give the required parameters for the normal distribution; in this case the mean and standard deviation. This carries out a one-sample test because you are comparing to a standard distribution. Note, too, that you get an error message because you have tied values in your sample. You could create a normal distributed sample “on the fly” and compare this to your sample like so: Now in this example you have run a two-sample test because you have effectively created a new sample using the pnorm () command. In this case the parameters of the normal distribution are contained in the pnorm () command itself. You can also test to see if the distribution is less than or greater than your comparison distribution by adding the alternative = instruction; you use less or greater because the default is two. sided.

Earlier you looked at histograms and density plots to visualize a distribution; you can perhaps estimate the appearance of a normal distribution by its bell-shaped appearance. However, it is easier to judge if you can get your distribution to lie in a straight line. To do that you can use quantile-quantile plots (QQ plots). Many statisticians prefer QQ plots over strictly mathematical methods like the Shapiro-Wilk test for example.

R语言代考

统计代写|R语言代写R language代考|Other Distributions

>比诺姆⁡(C(3,6,9,12)， 尺寸=17， 概率=0.5)
[1] 0.0063630.1661530.6854710.975479

>q吨(0.975,dF=C(5,10,100, 信息))
[1] 2.5712.2281.9841.960
>(1−点⁡(C(1.6,1.9,2.2), 自由度=信息))∗2
[1]0.109600.057430.02781

统计代写|R语言代写R language代考|The Kolmogorov-Smirnov Test

Kolmogorov-Smirnov 检验使您能够比较两个分布。这意味着您可以将样本与“已知”分布进行比较，也可以比较两个未知分布以查看它们是否相同；实际上你是在比较形状。

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