Normal distribution, Advanced Statistics

Assignment Help:

Your first task is to realize two additional data generation functions. Firstly, extend the system to generate random integral numbers based on normal distribution. You need to study Data Generator's structure and extend number generation type to activate normal distribution. The interface needs to obtain both mean and sigma as shown in Figure 1. Consider the code found here which is reproduced below for your convenience:
function gauss() {
// N(0,1)
// returns random number with normal distribution:
// mean=0
// std dev=1

// auxiliary vars
$x=random_0_1();
$y=random_0_1();
// two independent variables with normal distribution N(0,1)
$u=sqrt(-2*log($x))*cos(2*pi()*$y);
$v=sqrt(-2*log($x))*sin(2*pi()*$y);
// i will return only one, couse only one needed
return $u;
}
function gauss_ms($m=0.0,$s=1.0) {
// N(m,s)
// returns random number with normal distribution:
// mean=m
// std dev=s
return gauss()*$s+$m;
}
function random_0_1() {
// auxiliary function
// returns random number with flat distribution from 0 to 1
return (float)rand()/(float)getrandmax();
}
Notice that the return value of the above code is a floating value. You can round it to nearest integer by adding a "rounding option" to the interface.

773_normal distribution.png

Figure: Functions added to Data Generator

Next, realize one form of skewed distribution that approximates Pareto Principle. Consider a skewed access pattern often evidenced in data applications such that s percent of accesses would go to (100 - s) percent of data items. For instance, a typical "80-20 rule" for 1000 accesses over 500 data items means that about 800 accesses (80% of accesses) go to a specific set of about 100 items (20% of data items). In our case, data generation should be based on independent repeated trials, not as all trials once in a batch. Therefore, implementing strict Pareto Principle is difficult. Instead, we can approximate access pattern generation by the following method:

• skew generation function receives a range r and a skew factor s as parameter, both of which are integers and r must be larger 1 while s must be between 50 and 100.

• data elements are considered to have unique IDs in the range [1, r], in which elements are listed in an increasing order of IDs such as 1, 2, 3, ..., r.

• skew generation function produces an integer value between 1 and r representing a data access in the following manner:

1. skewed access will go to the top portion of the elements, that is, those between 1 and t = r × (100 - s) / 100.

2. draw a random number p from uniform distribution between 0 and 99.

3. if p falls in less than s, i.e., [0, s - 1], the top portion of elements [1, t] is accessed.

4. otherwise the access goes to [t + 1, r].

Above illustration should be sufficient to provide you with the concrete requirement for the two frequently utilized data generation. Figure 1 and 2 shows interface and sample output respectively. In these figures, rounding to integer is applied automatically. A checkbox should be added to the interface so that users can choose whether values generated are rounded or not. Notice that this development is not from scratch, but is "reverse engineering" of already developed product. Addition of the above functions to Data Generator is easily done. You should look into the contents of docs/data_types.php.

2439_normal distribution1.png

Figure: Generated data example


Related Discussions:- Normal distribution

Breusch-pagan test, The Null Hypothesis - H0:  There is no heteroscedastici...

The Null Hypothesis - H0:  There is no heteroscedasticity i.e. β 1 = 0 The Alternative Hypothesis - H1:  There is heteroscedasticity i.e. β 1 0 Reject H0 if Q = ESS/2  >

Probit analysis, Probit analysis  is the technique most commonly employed i...

Probit analysis  is the technique most commonly employed in the bioassay, specifically toxicological experiments where the group of animals is subjected to known levels of a toxin

Hypergeometric distribution, Hypergeometric distribution is t he probabili...

Hypergeometric distribution is t he probability distribution related with the sampling without replacement from the population of finite size. If the population comprises of r ele

Queuing theory, 1) Let N1(t) and N2(t) be independent Poisson processes wit...

1) Let N1(t) and N2(t) be independent Poisson processes with rates, ?1 and ?2, respectively. Let N (t) = N1(t) + N2(t). a) What is the distribution of the time till the next epoch

Ain why the simulated result doesn''t have to be exact as the, ain why the ...

ain why the simulated result doesn''t have to be exact as the theoretical calculation

Continual reassessment method, Continual reassessment method: An approach ...

Continual reassessment method: An approach which applies Bayesian inference for determining the maximum tolerated dose in a phase I trial. The method starts by assuming a logistic

Institutional surveys, Institutional surveys are the surveys in which the ...

Institutional surveys are the surveys in which the primary sampling units are the institutions, for instance, hospitals. Within each of the sampled institution, a sample of the pa

Observation-driven model, Observation-driven model  is a term generally a...

Observation-driven model  is a term generally applied to models for the longitudinal data or time series which introduce within the unit correlation by specifying the conditional

Regression to the mean, Regression to the mean is the procedure first note...

Regression to the mean is the procedure first noted by Sir Francis Galton that 'each peculiarity in man is shared by his kinsmen, but on average to the less degree.' Hence the ten

Multivariate analysis of variance, Multivariate analysis of variance is th...

Multivariate analysis of variance is the procedure for testing equality of the mean vectors of more than two populations for the multivariate response variable. The method is dire

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd