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

Find distribution - expected value and variance, We are installing a router...

We are installing a router for our network. We believe that the time between the arrival of packets will be exponentially distributed with parameter R = 2 packets/second, and th

Explain Genetic algorithms, Genetic algorithms: The optimization events mo...

Genetic algorithms: The optimization events motivated by the biological analogies. The prime idea is to try to mimic the 'survival of the fittest' rule of the genetic mutation in

Markov chains.., a shop is selling laptops at regular price and at half pri...

a shop is selling laptops at regular price and at half price.If the laptops are regular price a day they will be at regular price tha day after with proba 2/3, if the laptops are a

Procrustes analysis, Procrustes analysis is a technique of comparing the a...

Procrustes analysis is a technique of comparing the alternative geometrical representations of a group of multivariate data or of the proximity matrix, for instance, two competing

Explain kendall''s tau statistics, Kendall's tau statistics : The measures ...

Kendall's tau statistics : The measures of the correlation between the two sets of rankings. Kendall's tau itself (τ) is the rank correlation coefficient based on number of inversi

Cluster sampling, Cluster sampling : A method or technique of sampling in w...

Cluster sampling : A method or technique of sampling in which the members of the population are arranged in groups (called as 'clusters'). A number of clusters are selected at the

Outliers - reasons for screening data, Outliers - Reasons for Screening Dat...

Outliers - Reasons for Screening Data Outliers are due to data entry errors, subject is not a member of the population that the sample is trying to represent, or the subject i

Explain post stratification adjustment, Post stratification adjustmen t: On...

Post stratification adjustmen t: One of the most often used population weighting adjustments used in the complex surveys, in which weights for the elements in a class are multiplie

Please answer this question, How large would the sample need to be if we ar...

How large would the sample need to be if we are to pick a 95% confidence level sample: (i) From a population of 70; (ii) From a population of 450; (iii) From a population of 1000;

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