We discuss several statistical properties of the new proposed Log-Logistic Erlang (LLogE) distribution. Additionally we analyse birth, death oscillation of Canadian provinces in depth as well as the correlation between birth and death and those with temperature that has been collected from center of population of each provinces. While the focus of this study is on Canada, temperature may have a global influence on fertility. Even if there is no consensus how seasonality of birth phenomenon modelled, yet environmental factors specifically temperature, plays a role in explaining the seasonality observed in birth in many countries over many years. There are many other factors other than temperature that plays role to disentangle the shocks presents in birth. Our research offers unique insights by exploring the effects of environmental factors on monthly and daily birth and death oscillations using spectral and correlation analysis during 2011 and 2019.