In this paper, we produced a new family of distribution called Gull Alpha Power Family of distributions (GAPF). A Special case of GAPF is derived by considering the Weibull distribution as a baseline distribution called Gull Alpha Power Weibull distribution (GAPW). The suitability of the proposed distribution derives from its ability to model both the monotonic and non-monotonic hazard rate functions which are a common practice in survival analysis and reliability engineering. Various statistical properties were derived in addition to their special cases. The unknown parameters of the model are estimated using the maximum likelihood method. Moreover, the usefulness of the proposed distribution is supported by using two real lifetime data sets as well as simulated data.

In this paper, a new modification of the Lomax distribution is considered named as Lomax exponential distribution (LE). The proposed distribution is quite flexible in modeling the lifetime data with both decreasing and increasing shapes (non-monotonic). We derive the explicit expressions for the incomplete moments, quantile function, the density function for the order statistics etc. The Renyi entropy for the proposed distribution is also obtained. Moreover, the paper discusses the estimates of the parameters by the usual maximum likelihood estimation method along with determining the information matrix. In addition, the potentiality of the proposed distribution is illustrated using two real data sets. To judge the performance of the model, the goodness of fit measures, AIC, CAIC, BIC, and HQIC are used. Form the results it is concluded that the proposed model performs better than the Lomax distribution, Weibull Lomax distribution, and exponential Lomax distribution.

The main goal of the current paper is to contribute to the existing literature of probability distributions. In this paper, a new probability distribution is generated by using the Alpha Power Family of distributions with the aim to model the data with non-monotonic failure rates and provides a better fit. The proposed distribution is called Alpha Power Exponentiated Inverse Rayleigh or in short APEIR distribution. Various statistical properties have been investigated including they are the order statistics, moments, residual life function, mean waiting time, quantiles, entropy, and stress-strength parameter. To estimate the parameters of the proposed distribution, the maximum likelihood method is employed. It has been proved theoretically that the proposed distribution provides a better fit to the data with monotonic as well as non-monotonic hazard rate shapes. Moreover, two real data sets are used to evaluate the significance and flexibility of the proposed distribution as compared to other probability distributions.

Due to the advance computer technology, the use of probability distributions has been raised up to solve the real life problems. These applications are found in reliability engineering, computer sciences, economics, psychology, survival analysis, and some others. This study offers a new probability model called Marshall–Olkin Extended Gumbel Type‐II (MOEGT‐II) which can model various shapes of the failure rate function. The proposed distribution is capable to model increasing, decreasing, reverse J‐shaped, and upside down bathtub shapes of the failure rate function. Various statistical properties of the proposed distribution are derived such as alternate expressions for the density and distribution function, special cases of MOEGT‐II distribution, quantile function, Lorenz curve, and Bonferroni curve. Estimation of the unknown parameters is carried out by the method of maximum likelihood. A simulation study is conducted using three different iterative methods with different samples of sizes n. The usefulness and potentiality of the MOEGT‐II distribution have been shown using three real life data sets. The MOEGT‐II distribution has been demonstrated as better fit than Exponentiated Gumbel Type‐II (EGT‐II), Marshall–Olkin Gumbel Type‐II (MOGT‐II), Gumbel Type‐II (GT‐II), Marshall–Olkin–Frechet (MOF), Frechet (F), Burr III, Log Logistic (LL), Beta Inverse Weibull (BIW), and Kumaraswamy Inverse Weibull (KIW) distributions.

Background: Immunization is one of the most effective public health initiatives, saving millions of lives and lowering the risk of diseases such as diphtheria, tetanus, influenza, and measles. Immunization saves an estimated 2–3 million lives per year. A study of the regional variations in incomplete immunization will be useful in identifying gaps in the performance of immunization programs that are not noticed by standard vaccination programs monitoring. The primary goal of this study was to identify factors influencing child immunization status and to examine regional variations in incomplete immunization among children aged 12 to 23 months in Pakistan. Methods: For the current study, the data were taken from the Demographic and Health Survey for Pakistan (PDHS 2017–2018). Ever-married women who had children aged 12–23 months were included in this study. The immunization status of children was used as an outcome variable. In order to determine the effects of different factors on incomplete immunization, multilevel logistic model was used. To study the geographical variation of incomplete immunization, hotspot analysis was done using ArcGIS 10.7 and SaTScan software and to identify significant predictors of incomplete immunization, GWR 4 software was used. Results: Place of delivery, gender of child, mother’s educational level and region were identified as significant determinants of incomplete immunization of children in Pakistan. Chances of incomplete immunization of children were found significantly lower for educated mothers (AOR = 0.52, 95% CI 0.34–0.79) and mothers who had delivered children in the health facilities (AOR = 0.51, 95% CI 0.32–0.83). Female children were more likely (AOR = 1.44, 1.95% CI 1.04–1.99) to be incompletely immunized as compared to male children. FATA (AOR = 11.19, 95% CI 4.89–25.6), and Balochistan (AOR = 10.94, 95% CI 5.08–23.58) were found at the highest risk of incomplete immunization of children as compared to Punjab. The significant spatial heterogeneity of incomplete immunization was found across Pakistan. The spatial distribution of incomplete immunization was clustered all over Pakistan. The high prevalence of incomplete immunization was observed in Balochistan, South Sindh, North Sindh, South KPK, South FATA, Gilgit Baltistan, Azad Jammu Kashmir, South and East Punjab. Drang and Harcho were identified as hotspot areas of incomplete immunization in Gilgit Baltistan. Secondary clusters with a high risk of incomplete immunization were found in regions Balochistan, Sindh and FATA. Conclusion: Gender biasedness towards female children, regarding complete immunization of children prevailed in Pakistan. Spatial heterogeneity was also found for incomplete immunization of children. To overcome the problem access to health facilities is the foremost step. Government should target hotspot areas of incomplete immunization of children to provide primary health care facilities by opening health care units in these areas. The government in collaboration with the media should launch awareness campaigns in those areas to convince people that complete immunization is the right of every child regardless of gender.

Background: Every year, 2 million babies are stillborn in the world. Globally, there has been a decline in the stillbirth rate of 2%. Despite advancements in prenatal care and the implementation of new medical technologies, the incidence of early stillbirths remains unchanged. A slight decrease in the rate of late-term stillbirth has been observed. Pakistan ranked third in South Asia for having the highest stillbirth rate. Compared to its neighbors and other developing nations, Pakistan has shown a lack of progress in reducing maternal and neonatal fatalities. Therefore, the purpose of this study is to use a multivariate decomposition analysis to examine the trends and factors that have contributed to the change in the stillbirth rate over time.Methods: To conduct this study, we used a secondary data analysis approach and analyzed data from the Pakistan Demographic and Health Survey (PDHS) of 2012–2013 and 2017–2018). For the analysis, a total sample of 15,068 births in 2017–2018 and 13,558 births in the PDHS from 2012 to 2013 were taken into account. Using the MVDCMP function within STATA version 15 statistical software, a logit-based multivariate decomposition model was fitted to determine the variables that influence the change in stillbirth. The current study used two cross-sectional surveys to identify important risk factors for stillbirths.Results: Over the past 5 years, Pakistan's stillbirth rate has risen from 3.98 to 5.75%. According to the total multivariate decomposition analysis, the change in coefficient (change in the effect of attributes) accounted for 81.17% of the overall change in the proportion of stillbirths. In contrast, the change in endowment was not statistically significant. Changes in maternal education, individual and community-level wealth status, and mode of delivery all significantly impacted the rate of stillbirths over time.Conclusion: Stillbirths increased in Pakistan from 2012 to 2017. Stillbirths are observed more frequently for women residing in Punjab, Sindh, and rural areas. A major concern that is directly related to the prevalence of stillbirths in Pakistan is the lack of accessible, affordable, and high-quality maternal healthcare facilities. Older, overweight, and uneducated women are more likely to have stillbirths than women who deliver vaginally. High parity and short birth intervals also accelerated the rate of stillbirths. An effective remedy to control stillbirths is the provision of accessible and affordable healthcare services. Awareness campaigns for the health education of pregnant women should focus on raising awareness to support better pregnancy outcomes for poor women living in communities with higher education levels. The risk of stillbirth can be reduced by offering free diagnostics for early detection of birth complications in low-resource settings and referring these cases to knowledgeable gynecologists for safe delivery.