by Parameshwar V Pandit and Shubhashree Joshi
Original Research
The paper deals with the estimation of multicomponent system reliability where the system has k components with their strengths X1, X2, … Xk being independently and identically distributed random variables and each component is experiencing a random stress Y. The s-out-of-k system is said to function if atleast s out of k (1 ≤ s ≤ k) strength variables exceed the random stress. The reliability of such a system is derived when both strength and stress variables follow generalized Pareto distribution. The system reliability is estimated using maximum likelihood and Bayesian approaches. The maximum likelihood estimators are derived under both simple random sampling and ranked set sampling schemes. Lindley's approximation technique is used to get approximate Bayes estimators. The reliability estimators obtained from both the methods are compared by using mean squares error criteria and real data analysis is carried out to illustrate the procedure.
American Journal of Applied Mathematics and Statistics. 2018, 6(5), 210-217. DOI: 10.12691/ajams-6-5-5
Pub. Date: October 26, 2018
8398 Views2248 Downloads
by Grine Azedine
Original Research
In this paper, a bivariate distribution with a two-parameter exponential conditional is obtained. A multivariate form of the result is also attained under the joint independence of components assumption. A maximum Likelihood method of estimation is provided as well as the intervals of confidence for the parameters of this bivariate distribution. The pdf of the order statistics and concommitants are also derived.
American Journal of Applied Mathematics and Statistics. 2018, 6(5), 201-209. DOI: 10.12691/ajams-6-5-4
Pub. Date: October 14, 2018
8447 Views1573 Downloads
by Pius Miri Ng’ang’a, Antony Waititu Gichuhi, Antony Wanjoya and Thomas Mageto
Original Research
Artificial Neural Network (ANN) is a parallel connection of a set of nodes called neurons which mimic biological neural system. Statistically, ANN represents a class of non-parametric models which is capable of approximating a non-linear function by a composition of low dimensional ridge functions. This study aimed at modeling diabetes mellitus among adult Kenyan population using 2015 stepwise survey data from Kenya National Bureau of Statistics. Data analysis was carried out using R statistical software version 3.5.0. Among the input variables Age, Sex, Alcoholic status, Sugar consumption, Physical Inactivity, Obesity status, Systolic and Diastolic blood pressure had a significant relationship with diabetic status at 5% level of significance. A multi layered feed-forward neural network with a back propagation algorithm and a logistic activation function was used. Considering a parsimonious model, the model selected had the eight input variables with two neurons in the hidden layer since it gave a minimum MSE of 0.0580 reported. 75% of data was used for training while 25% was used for testing. The sensitivity of the trained network was reported as 75% while specificity was 94.29%. The overall accuracy of the model was 84.64% . This implied that the model could correctly classify an individual as either diabetic or not with an accuracy rate of 84.64%. A 10-fold cross validation was carried out and an average MSE of 0.0686 reported. Kolmogorov-Smirnov test of normality was carried out and at 5% level of significance, for most parameter estimates, we failed to reject the null hypothesis and concluded that the network parameter estimates were asymptotically normal and consistent. With a good choice of risk factors for diabetes, neural network structures could be successfully used to accurately model diabetes melitus among Kenyan adult population.
American Journal of Applied Mathematics and Statistics. 2018, 6(5), 186-200. DOI: 10.12691/ajams-6-5-3
Pub. Date: October 07, 2018
14123 Views2600 Downloads2 Likes
by B. Srinivasa Rao, P. Sricharani and M.S. Ravikumar
Original Research
The Dagum distribution is considered as a life time random variable of a product whose lots are to be decided for acceptance or otherwise on the basis of sample lifetimes drawn from the lot. The sample is divided into various groups in order to develop a group sampling plan in such a way that the life testing experiment is terminated as soon as the first failure in each group is observed. The acceptance criterion based on the theory of order statistics is proposed.
American Journal of Applied Mathematics and Statistics. 2018, 6(5), 181-185. DOI: 10.12691/ajams-6-5-2
Pub. Date: September 19, 2018
7802 Views2126 Downloads4 Likes
by Noora Shrestha
Original Research
Neck circumference (NC) measurement is one of the simple screening measurements, that can be used as a marker of upper body fat distribution to notice overweight. The objective of this study is to evaluate the relationship between NC and overweight/obesity. In this cross-sectional study a total 198 college students (120 Female, 78 Male) aged 18-23 years were participated using convenience method. Anthropometric measurements of students were measured according to the guidelines of world health organization. Students with NC ≥37 cm for male and ≥34 cm for female and BMI ≥ 25 kg/m2 are identified as overweight. The percentages of the male and female students with BMI ≥ 25 kg/m2 were 9% and 15.8% respectively and with high NC were 47.4% and 23.3 % respectively. In both male and female students, there were significant and positive correlation of neck circumference with body weight (male, r=0.572; female, r=0.629; p=0.001), waist circumference (male, r= 0.407; female, r= 0.623; p=0.001), hip circumference (male, r=0.546; female, r=0.579; p=0.001), BMI (male, r= 0.532; female, r= 0.588; p=0.001), waist to hip ratio (female, r = .376; p= .001), and waist to height ratio (male, r= 0.33; female, r= 0.574; p=0.001). A significant and independent association was found between NC and overweight levels using multiple regression analysis in young adults. This study indicates neck circumference is a simple screening measure that can be used to identify overweight/obesity.
American Journal of Applied Mathematics and Statistics. 2018, 6(5), 176-180. DOI: 10.12691/ajams-6-5-1
Pub. Date: September 18, 2018
11310 Views2966 Downloads18 Likes