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

Public network, This is given by common network e.g. Phone Company. The pub...

This is given by common network e.g. Phone Company. The public networks are those networks, which are given by common carriers. It can be a telephone company or an other organizati

Explain healthy worker effect, Healthy worker effect : The occurrence where...

Healthy worker effect : The occurrence whereby employed individuals tend to have lower mortality rates than those who are unemployed. The effect, which can pose the serious problem

Naor''s distribution, Naor's distribution is the discrete probability dist...

Naor's distribution is the discrete probability distribution which arises from the following model; Assume an urn contains n balls of which one is red and the remainder is whit

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

Describe prior distribution, Prior distributions : The probability distribu...

Prior distributions : The probability distributions which summarize the information about a random variable or parameter known or supposed at a given time instant, prior to attaini

MC0074 –Statistical and Numerical methods using C++, Write a c++ program to...

Write a c++ program to find the sum of 0.123 ? 103 and 0.456 ? 102 and write the result in three significant digits

Link functions, Link functions: The link function relates the linear p...

Link functions: The link function relates the linear predictor ηi to the expected value of the data. In classical linear models the mean and the linear predictor are identical

Logistic regression - computing log odds without probabiliti, Please help w...

Please help with following problem: : Let’s consider the logistic regression model, which we will refer to as Model 1, given by log(pi / [1-pi]) = 0.25 + 0.32*X1 + 0.70*X2 + 0.

Parks test, The Null Hypothesis - H0: β 1 = 0 i.e. there is homoscedastici...

The Null Hypothesis - H0: β 1 = 0 i.e. there is homoscedasticity errors and no heteroscedasticity exists The Alternative Hypothesis - H1: β 1 ≠ 0 i.e. there is no homoscedasti

Average age at death, Average age at death : A ?awed statistic summarizing ...

Average age at death : A ?awed statistic summarizing expectancy of the life and other aspects of the mortality. For instance, a study comparing average age at the death for male sy

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