Highlights• The article focuses on a class of inverted exponential distribution.• The proposed distribution aims at proposing a better flexible model for lifetime data.• The performance is validated by application of real life data in existing literature.• Results indicate that the new model competes favourably well with other distributions.

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A new flexible univariate probability distribution was defined in this paper. The new distribution is so called the ‘exponentiated Gumbel–Weibull {logistic} distribution’ and it arose by using the exponentiated Gumbel distribution to generate a generalized Weibull distribution using the logit function or the quantile function of the logistic distribution as a link. The new distribution was observed to be both unimodal and bimodal as well as exhibits various shape and tail properties consistent with data arising from several real life phenomena. A detail study of its statistical properties was carried out and the maximum likelihood method was used in the estimation of its parameters. The new distribution was applied in fitting the reported daily number of infections due to the COVID-19 pandemic in Nigeria. Five other datasets were further used to ascertain the flexibility of the new distribution in fitting data sets with different statistical properties.

In this paper, we considered the different strategies that generate the optimal wealth on investment. The strategy examine depends on the utility function an investor is willing to adopt, say H * at time N in every 2n possible states; in an N period setting. Negative exponential, logarithm, square root and power utility functions were established, as the market structures changed according to a Markov chain through a martingale approach. The problem of maximization is solved via Lagrange method. The performance of the investment from day-today is driven by the ratio of the risk neutral probability and the probability of rising to falling.