American Journal of Applied Mathematics and Statistics

The objective of this work is to study effect of environmental tax on emitters to attain a pollution free environment. In this paper, an attempt has been made to study the effect of environmental tax to control carbon dioxide (a global warming gas) concentration in the atmosphere using a nonlinear mathematical model. It is assumed that the environmental tax is levied only when the concentration of carbon dioxide crosses a threshold level over which it is harmful to our environment. Analytically, it is shown that the concentration of carbon dioxide decreases as the rate of environmental tax increases. The variation of carbon dioxide concentration (with and without environmental tax) has also been shown in a plot to confirm analytical results. Further, carbon dioxide concentration can also be reduced by greenbelt (leafy trees) plantation. It is shown, analytically and numerically, that carbon dioxide concentration decreases as its rate of interaction (absorption) with leafy trees increases.

American Journal of Applied Mathematics and Statistics. 2016, 4(1), 16-23. DOI: 10.12691/ajams-4-1-3
Pub. Date: February 29, 2016

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Properties of Doubly-Truncated Fréchet Distribution

by Salah H Abid

Original Research

The truncated distributions has been widely studied, primarily in life-testing and reliability analysis. Most work has assumed an upper bound on the support of the random variable, i.e. the space of the distribution is (0, d). We consider a doubly-truncated Fréchet random variable restricted by both a lower (c) and upper (d) truncation point. We provide forms for the density, cumulative distribution function (CDF), hazard function, characteristic function, rth raw moment, mean, mode, median, variance, skewness, kurtosis, Shannon entropy function, relative entropy and quantile function. We also consider the generating issues. This paper deals also with the determination of R = P[Y < X] when X and Y are two independent doubly truncated Fréchet distributions (DTFD) with different scale parameters, different shape parameters but the same truncations parameters. Different methods to estimate doubly truncated Fréchet distribution parameters are studied, Maximum Likelihood estimator, Moments estimator, Percentile estimator, least square estimator and weighted least square estimator. An empirical study is conducted to compare among these methods.

American Journal of Applied Mathematics and Statistics. 2016, 4(1), 9-15. DOI: 10.12691/ajams-4-1-2
Pub. Date: January 26, 2016

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Goodness-of-fit-test for Exponential Power Distribution

by A. A. Olosunde and A. M. Adegoke

Original Research

Given a set of data, one of the statistical issues is to see how well the data fit into postulated model. This technique necessitates the corresponding table of the probability distribution for the proposed model. In this paper, we examined, to what limit of p can normal approximate this sample without falling into type I error (i.e. a random variable x having normal distribution when indeed it has exponential power distribution with estimated parameter p). We also present the goodness-of-fit test for exponential power distribution using the conventional testing methods which are discussed, one is Pearson’s χ2 test and the other one is kolmogorov-Smirnov test. An example in poultry feeds data and a simulation example are included, comparison with the fitting of the normal distribution is also examined for further illustration.

American Journal of Applied Mathematics and Statistics. 2016, 4(1), 1-8. DOI: 10.12691/ajams-4-1-1
Pub. Date: January 15, 2016

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