The classical linear model is commonly used to model the relationship between a response variable and a set of explanatory variables. The normality assumption is usually required so as to ease the hypothesis testing for the various linear regression models but it can be misleading for a proportional response variable that is bounded. This makes the ordinary least squares regression inappropriate for a regression model with a bounded dependent variable. This research proposes the fractional beta regression model as an alternative to help examine the determinants of post-harvest loss management of maize produce for farmers in Kenya. The response variable (Post-Harvest Loss Coefficient (PHLC)) is assumed to have a mixed continuous-discrete distribution with probability mass between zero and one. The fractional beta distribution is used to describe the continuous component of the model, since its density has a wide range of different shapes depending on the values of the two parameters that index the distribution. The study uses a suitable parameterization of the beta law in terms of its mean and a precision parameter, the parameters of the mixture distribution shall be modeled as functions of regression parameters. The considered parameters are Agriculture, Storage, Education, Fumigation and Transport. Inference on parameters, model diagnostics and model selection tools for the fractional beta regression is also be provided. Data used for this research was purely primary data which was collected from Uasin Gishu County, Kenya maize farmers through administration of a research questionnaire.

Mathematical literacy is the ability to use numbers to help solve real-world problems. It focuses on pupils' ability to analyze, justify and communicate ideas effectively with regard to formulating, solving and interpreting Mathematical problems in a variety of forms and situations. The study modeled above threshold scores in mathematics among school pupils as an indicator for being mathematically literate. Modeling was on the inter-arrival times for pupils scoring above threshold scores (Mathematics mean score) for a given sample of pupils in their mid and end of term examinations. The Poisson distribution has been widely used as a statistical procedure for modeling inter-arrival times for count data outcomes. However, for heavy-tailed inter-arrival times of successive outcomes, the Poisson distribution exhibits an empirical observational failure thus setting up a framework for the use of other distributions that can handle such heavy-tailed data. The study used the generalized Gumbel and Weibull inter-arrival time distributions which were assumed to nest the standard Poisson distribution in which Weibull inter-arrival gave a better fit to the data. Data used was secondary data on pupil performance in Mathematics in relation to other subjects from Acacia Crest School.

Anopheles funestus and Anopheles gambiae are malaria vector mosquitoes.Knowing their resting behavior is important for implementing control methods. The aim of this study was to investigate the resting behaviour of the two malaria mosquitoes. The study was conducted in Kilombero River Valley and mosquitoes were collected using indoor and outdoor traps from 2012-2015. Poisson mixed models were used to quantify the impact of environment variables on resting behaviour. A log ratio rate between the type of trap and its interaction with environmental variables was used to determine if there was a change over time in the resting behaviour. A total of 4696 mosquitoes were resting indoors of which 57% were A. funestus and 43% were A. gambiae. Similarly, a total of 12,028 mosquitoes were resting outdoor of which 13% were A. funestus and 87% were A. gambiae. Temperature was significant and affected the resting behaviour of A. funestus. Humidity, saturation deficit and temperature were significant variables influencing the resting behaviour of A. gambiae. A. funestus was resting indoor while A. gambiae was resting outdoor over time generally. The findings of this study on the effects of environmental variables and the variations in the resting behaviour of A. gambiae and A. funestus could be used as a guide to implementing appropriate intervention measures such as indoor residential spraying (IRS), insecticide treated nets (ITNs) and mosquito repellents.

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