The Normal, Chi-squared and Student’s T Distributions in the Teaching of Biostatistics for Students of Medical Sciences
Rafael Mauro Avila Avila,
Maria del Carmen Exposito Gallardo,
Julio Cesar Pino Tarrago
Issue:
Volume 10, Issue 2, April 2022
Pages:
15-21
Received:
21 December 2021
Accepted:
14 January 2022
Published:
8 April 2022
DOI:
10.11648/j.sjams.20221002.11
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Abstract: The normal, Chi-Squared and Student’s t distribution are three of the most important in the teaching learning process of Biostatistics for the specialty of Medicine. However, the absence of a deductive approach in the introduction to the topics, makes difficult to understand its origin. From the starting point of the systems of continue distributions of probability, it is proposed an alternative way to introduce the normal distribution in general and standard form, as well as the analytic expressions for the Chi-Squared and Student’s T distributions. Some epistemic gaps in the treatment of the thematic are identified by means of the analytic synthetic and documentary review methods. The essential objectives consist of the deduction the mathematical expression of such distribution as well as to value the possibility to introduce the basic elements of the used procedure, in the program of Biostatistics, emphasizing the notions of Differential Calculus developed in previous stage to the Integral Calculus. The essential conclusion is associated to the contribution of the suggested approach to the rigor and harmony of mathematical statistic knowledge in the discipline, although some concepts of Mathematical Analysis are necessary in order to facilitate the understanding of the practical applications in the career of Medicine and in other branches of the research in biomedical sciences.
Abstract: The normal, Chi-Squared and Student’s t distribution are three of the most important in the teaching learning process of Biostatistics for the specialty of Medicine. However, the absence of a deductive approach in the introduction to the topics, makes difficult to understand its origin. From the starting point of the systems of continue distributio...
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Extension of Power Mean and Logarithms Mean
Yisa Anthonio,
Abimbola Abolarinwa,
Abdullai Abdurasid,
Kamal Rauf,
Michael Adeniyi,
Adeyinka Ogunsanya,
Christian Iluno
Issue:
Volume 10, Issue 2, April 2022
Pages:
22-27
Received:
4 February 2022
Accepted:
7 March 2022
Published:
20 April 2022
DOI:
10.11648/j.sjams.20221002.12
Downloads:
Views:
Abstract: Logarithms are indispensable in the revision of mathematics which are basic components tools in the theory of mathematical analysis. Logarithms have playing acute fundamental role in the study of the properties of power and arithmetic means as well as inequalities of Logarithms with their bound. This paper shows the properties of logarithms mean, power mean, arithmetic mean, Harmonic mean, geometric mean and later we use Minkowski’s inequality and Hölder’s inequality to establish the modified means. In the paper, we obtained the generalization of power mean, logarithms mean, arithmetic mean, Harmonic mean and geometric mean. The methodology adopted are Minkowski’s inequality and Hölder’s inequality to establish some means of order α of two distincts. These inequalities further generalize some existing results. This research work also demonstrated the importance of the Minkowski’s inequality and Hölder’s inequality over existing arithmetic mean, Harmonic mean and geometric mean and further extend the generalization to weighted logarithms mean. Hence, this article distinguished some present results on power mean, logarithms means and acquired more robust means by engaging modified Minkowski’s inequality and Hölder’s inequality with some ordinary theorems. The modified Minkowski’s inequality on power and logarithms mean further extends the generalized weighted logarithms mean of order α of two distincts.
Abstract: Logarithms are indispensable in the revision of mathematics which are basic components tools in the theory of mathematical analysis. Logarithms have playing acute fundamental role in the study of the properties of power and arithmetic means as well as inequalities of Logarithms with their bound. This paper shows the properties of logarithms mean, p...
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