Abstract
A three-parameters continuous distribution, namely, Power Lomax distribution (POLO) is proposed and studied for remission times of bladder cancer data. POLO distribution accommodate both inverted bathtub and decreasing hazard rate. Several statistical and reliability properties are derived. Point estimation via method of moments and maximum likelihood and the interval estimation are also studied. The simulation schemes are calculated to examine the bias and mean square error of the maximum likelihood parameter estimators. Finally, a real data application about the remission time of bladder cancer is used to illustrate the usefulness of the proposed distribution in modelling real data application. The characteristics of the fitting data using the proposed distribution are compared with known extensions of Lomax distribution. The comparison showed that the POLO distribution outfit most well-known extensions of Lomax distribution.
Highlights
The Lomax (1954), or Pareto II, distribution introduced originally for modeling business failure data, it has been widely applied in a variety of contexts
The structural characteristics of Power Lomax distribution (POLO) distribution including the behavior of the probability density function, the hazard rate function, the reversed hazard rate function, the residual life, the entropy measures, the stress strength parameter, the moments and the associated moments, the order statistics and extreme values and the mean deviation and quantile function are studied in section “Structural characteristics”
Maximum likelihood estimation Let x1, x2, ..., xn be a random sample of size n from the POLO distribution with probability density function (PDF) given by Eq (11)
Summary
The Lomax (1954), or Pareto II, distribution introduced originally for modeling business failure data, it has been widely applied in a variety of contexts. The distribution has been used for modeling different data which studied by so many authors, Harris (1968) used Lomax distribution for income and wealth data, Atkinson and Harrison (1978) used it for modelling business failure data, while Corbelini et al (2007) used it to model firm size and queuing problems It has found application in the biological sciences and even for modelling the distribution of the sizes of computer files on servers, Holland et al (2006). A random variable X has the Lomax distribution with two parameters α and λ if it has cumulative distribution function (CDF) (for x > 0) given by. The structural characteristics of POLO distribution including the behavior of the probability density function, the hazard rate function, the reversed hazard rate function, the (reversed) residual life, the entropy measures, the stress strength parameter, the moments and the associated moments, the order statistics and extreme values and the mean deviation and quantile function are studied in section “Structural characteristics”. A real data life application of bladder cancer data are illustrated the potential of POLO distribution compared with other distributions in section “Application”
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