The Sudden Infant Death Syndrome (SIDS) was defined in 1969 by Beckwith as sudden death of an infant or young child, unexpected by medical history, remaining unexplained after thorough autopsy/death-scene investigation. Recently researchers have used the general terms Sudden Unexplained Death in Infancy (SUDI) and Sudden Unexpected Infant Death (SUID) as "umbrella-terms" covering unexplained deaths (SIDS); sudden deaths for which SIDS risk factors present but insufficient cause is found; and sudden deaths for which sufficient cause is found. A characteristic feature of such deaths is that, 24-hours before death (or unexpected collapse that led to death), the caregivers were unaware that the baby was at increased risk of dying. The explainable cases include deaths from several recognized causes including infection, metabolic conditions, accidental and non-accidental injury, and various genetic or cardiac conditions as well as "Accidental Suffocation and Strangulation in Bed (ASSB)." SIDS is characterized by a ~50% male excess common to all respiratory infant deaths and a 4-parameter lognormal age distribution - thought to be unique and SIDS main distinguishing characteristic. In this article we model these data for age and/or gender distributions of SUDI/SUID and SIDS reported from the U.K., U.S., Norway and Germany. When pooled together with SIDS, these explained SUDI/SUID data on infant ages and gender have the same distributions as SIDS, indicating that the final mode of death for all SUDI or SUID may be a consequence of different paths to the same biological phenomena as for SIDS, though the mechanism of death remains unclear.